In this paper, we study a hydrodynamic system describing fluids with viscoelastic properties. After a brief examination of the relations between several models, we shall concentrate on a few analytical issues concerning them. In particular, we establish local existence and global existence (with small initial data) of classical solutions for an Oldroyd system without an artificially postulated damping mechanism.

This paper applies a diffuse-interface model to simulate the deformation of single drops in steady shear flows when one of the components is viscoelastic, represented by an Oldroyd-B model. In Newtonian fluids, drop deformation is dominated by the competition between interfacial tension and viscous forces due to flow. A fundamental question is how viscoelasticity in the drop or matrix phase influences drop deformation in shear. To answer this question, one has to deal with the dual complexity of nonNewtonian rheology and interfacial dynamics. Recently, we developed a diffuse-interface formulation that incorporates complex rheology and interfacial dynamics in a unified framework. Using a two-dimensional spectral implementation, our simulations show that, in agreement with observations, a viscoelastic drop deforms less than a comparable Newtonian drop. When the matrix is viscoelastic, however, the drop deformation is suppressed when the Deborah number De is small, but increases with De for larger De. This non-monotonic dependence on matrix viscoelasticity resolves an apparent contradiction in previous experiments. By analysing the flow and stress fields near the interface, we trace the effects to the normal stress in the viscoelastic phase and its modification of the flow field. These results, along with prior experimental observations, form a coherent picture of viscoelastic effects on steady-state drop deformation in shear.

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In this paper, we study a micro-macro model for polymeric fluid. The system involves coupling between the macroscopic momentum equation and a microscopic evolution equation describing the combined effects of the microscopic potential and thermofluctuation. We employ an energetic variation procedure to explore the relation between the macroscopic transport of the particles and the induced elastic stress due to the microscopic structure. For the initial data not far from the equilibrium, we prove the global existence and uniqueness of classical solutions to the system.

Deep learning is revolutionizing the mapping industry. Under lightweight human curation, computer has generated almost half of the roads in Thailand on Open-StreetMap (OSM) using high resolution aerial imagery. Bing maps are displaying 125 million computer generated building polygons in the U.S. While tremendously more efficient than manual mapping, one cannot map out everything from the air. Especially for roads, a small prediction gap by image occlusion renders the entire road useless for routing. Misconnections can be more dangerous. Therefore computer based mapping often requires local verifications, which is still labor intensive. In this paper, we propose to leverage crowd sourced GPS data to improve and support road extraction from aerial imagery. Through novel data augmentation, GPS rendering, and 1D transpose convolution techniques, we show almost 5% improvements over previous competition winning models, and much better robustness when predicting new areas without any new training data or domain adaptation.

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article info abstractKeywords: Ericksen-Leslie, nematic liquid crystals, thermodynamics consistency, global wellposedness, Besov regularity.MSC: 35Q30, 35Q35, 35Q79, 76A15.We derive a model describing the evolution of a nematic liquidcrystal material under the action of thermal effects. The first and second laws of thermodynamics lead to an extension of the general Ericksen-Leslie system where the Leslie stress tensor and the Oseen-Frank energy density are considered in their general forms. The work postulate proposed by Ericksen-Leslie is traduced in terms of entropy production. We finally analyze the global-in-time well-posedness of the system for small initial data in the framework of Besov spaces.5.4. The temperature equation 36 5.5. Passage to the limit 42 5.6. Uniqueness 42 6. Appendix 43 References 49 IntroductionThe main aim of this paper is to derive and analyze an evolutionary PDE's-system modeling the dynamics of nematic liquid crystals. The model we are interested in extends the general Ericksen-Leslie theory, allowing a non-constant temperature. We derive such a model in accordance with the main laws of thermodynamics. Nowadays, the engineering and mathematical community is familiar with the concept of nematic liquid crystals. A nematic medium is a compound of fluid molecules, which has a state of matter between an ordinary liquid and a crystal solid. Although the centers of mass can freely translate as in a common fluid, the constitutive molecules present a privileged orientation. This alignment strongly interacts with the underlying flow of the nematic. Reinitzer discovered one of these materials in the 1888 and since then there have been numerous attempts to formulate continuum theories describing the time behavior of the flow. Ericksen and Leslie developed the most widely recognaized model during the 1960's in their pioneeric papers [7,8,22], generalizing the Oseen-Frank theory for the static case [14]. From the first mathematical success in analyzying the model performed by Lin and Liu [23] in the 1991, the dynamics theory of liquid crystal has become the new El Dorado of theoretical studies motivated by real-world applications. The well-posedness analysis in bounded domains [2,20,25] as well as in the whole space [6,15], has especially received high interest in the recent decades, both for what concerns the director theory and the Q-tensor framework. These results are often inspired by the ample literature concerning the Navier-Stokes equations, since any derivation of a consistent model for these anisotropic materials usually starts from the well-known conservation of mass and balances of linear and angular momentum. Despite a wide literature concerning the dynamics of nematic liquid crystals, to the best of our knowledge there are few papers dealing also with thermodynamic effects. Liquid crystals are mostly considered in an isothermal environment, which is sometimes unnatural. Indeed, as described by Stewart in [27], liquid phases are mainly induced by changing the temperature (thermotropic...

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