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Changyou Wang - One of the best experts on this subject based on the ideXlab platform.
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strong solutions of the compressible nematic liquid crystal flow
Journal of Differential Equations, 2012Co-Authors: Tao Huang, Changyou WangAbstract:Abstract We study strong solutions of the simplified Ericksen–Leslie system modeling compressible nematic liquid crystal flows in a domain Ω ⊂ R 3 . We first prove the local existence of a unique strong solution provided that the initial data ρ 0 , u 0 , d 0 are sufficiently regular and satisfy a natural Compatibility Condition. The initial density function ρ 0 may vanish on an open subset (i.e., an initial vacuum may exist). We then prove a criterion for possible breakdown of such a local strong solution at finite time in terms of blow up of the quantities ‖ ρ ‖ L t ∞ L x ∞ and ‖ ∇ d ‖ L t 3 L x ∞ .
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strong solutions of the compressible nematic liquid crystal flow
arXiv: Analysis of PDEs, 2011Co-Authors: Tao Huang, Changyou WangAbstract:We study strong solutions of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in a domain $\Omega \subset\mathbb R^3$. We first prove the local existence of unique strong solutions provided that the initial data $\rho_0, u_0, d_0$are sufficiently regular and satisfy a natural Compatibility Condition. The initial density function $\rho_0$ may vanish on an open subset (i.e., an initial vacuum may exist). We then prove a criterion for possible breakdown of such a local strong solution at finite time in terms of blow up of the quantities $\|\rho\|_{L^\infty_tL^\infty_x}$ and $\|\nabla d\|_{L^3_tL^\infty_x}$.
Peter Buhlmann - One of the best experts on this subject based on the ideXlab platform.
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on the Conditions used to prove oracle results for the lasso
Electronic Journal of Statistics, 2009Co-Authors: Sara Van De Geer, Peter BuhlmannAbstract:Oracle inequalities and variable selection properties for the Lasso in linear models have been established under a variety of different assumptions on the design matrix. We show in this paper how the different Conditions and concepts relate to each other. The restricted eigenvalue Condition [2] or the slightly weaker Compatibility Condition [18] are sufficient for oracle results. We argue that both these Conditions allow for a fairly general class of design matrices. Hence, optimality of the Lasso for prediction and estimation holds for more general situations than what it appears from coherence [5, 4] or restricted isometry [10] assumptions.
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on the Conditions used to prove oracle results for the lasso
arXiv: Statistics Theory, 2009Co-Authors: Sara Van De Geer, Peter BuhlmannAbstract:Oracle inequalities and variable selection properties for the Lasso in linear models have been established under a variety of different assumptions on the design matrix. We show in this paper how the different Conditions and concepts relate to each other. The restricted eigenvalue Condition (Bickel et al., 2009) or the slightly weaker Compatibility Condition (van de Geer, 2007) are sufficient for oracle results. We argue that both these Conditions allow for a fairly general class of design matrices. Hence, optimality of the Lasso for prediction and estimation holds for more general situations than what it appears from coherence (Bunea et al, 2007b,c) or restricted isometry (Candes and Tao, 2005) assumptions.
Richard D. James - One of the best experts on this subject based on the ideXlab platform.
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3d microstructures of sb2te3 precipitates in pbte matrix with prediction by a weak Compatibility Condition
1st International Conference on 3D Materials Science 2012 3DMS 2012, 2012Co-Authors: Xian Chen, Dominique Schryvers, Shanshan Cao, Teruyuki Ikeda, Vijay Srivastava, Jeffrey G Snyder, Richard D. JamesAbstract:We propose that a weak Compatibility Condition predicts the elongated directions for Widmanstatten type precipitates. The distribution of the elongated directions of precipitates lies on a family of crystallographically equivalent cones in 3D determined by a certain transformation stretch matrix obtained independently. A 3D visualization and digitization method is developed to show how the cone variants control the preferred growth directions during precipitation of Sb2Te3 in a (5 µm)3 PbTe matrix. A series of two-dimensional secondary electron images are acquired along the direction perpendicular to the imaging plane. By pixelating all the images and calculating the position vectors on the surface of each precipitate, the elongation directions are calculated using a 3-dimensional ellipsoidal fitting for 182 precipitates. The 3D plot of the elongation directions shows that their spacial orientations are close to four predicted cones with a standard deviation of 5.6°. The length along the elongation directions reveals an asymmetric distribution with a mean value of about 240 nm. The total volume fraction of the precipitates is 8.3 %. The average area of the precipitates per volume is 0.68 µ-1 by one point statistical calculation. These results build on our study presented in [1] by analyzing a significantly bigger data set and by including the length distribution and 1-point statistics.
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a weak Compatibility Condition for precipitation with application to the microstructure of pbte sb2te3 thermoelectrics
Acta Materialia, 2011Co-Authors: Xian Chen, Dominique Schryvers, Shanshan Cao, Teruyuki Ikeda, Vijay Srivastava, Jeffrey G Snyder, Richard D. JamesAbstract:We propose a weak Condition of Compatibility between phases applicable to cases exhibiting full or partial coherence and Widmanstatten microstructure. The Condition is applied to the study of Sb_2Te_3 precipitates in a PbTe matrix in a thermoelectric alloy. The weak Condition of Compatibility predicts elongated precipitates lying on a cone determined by a transformation stretch tensor. Comparison of this cone with the long directions of precipitates determined by a slice-and-view method of scanning electron microscopy combined with focused ion beam sectioning shows good agreement between theory and experiment. A further study of the morphology of precipitates by the Eshelby method suggests that interfacial energy also plays a role and gives an approximate value of interfacial energy per unit area of 250 dyn cm^(−1).
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Transmission electron microscopy investigation of microstructures in low-hysteresis alloys with special lattice parameters
Scripta Materialia, 2009Co-Authors: Rémi Delville, Dominique Schryvers, Zhiyong Zhang, Richard D. JamesAbstract:A sharp drop in hysteresis is observed for shape memory alloys satisfying the Compatibility Condition between austenite and martensite, i.e. λ2 = 1, where λ2 is the middle eigenvalue of the transformation strain matrix. The present work investigates the evolution of microstructure by transmission electron microscopy as the composition of the Ti50Ni50−xPdx system is systemically tuned to achieve the Condition λ2 = 1. Changes in morphology, twinning density and twinning modes are reported along with twinless martensite and exact austenite–martensite interfaces.
Hi Jun Choe - One of the best experts on this subject based on the ideXlab platform.
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global existence of the radially symmetric solutions of the navier stokes equations for the isentropic compressible fluids
Mathematical Methods in The Applied Sciences, 2005Co-Authors: Hi Jun ChoeAbstract:We study the isentropic compressible Navier-Stokes equations with radially symmetric data in an annular domain. We first prove the global existence and regularity results on the radially symmetric weak solutions with non-negative bounded densities. Then we prove the global existence of radially symmetric strong solutions when the initial data ρ 0 , u 0 satisfy the Compatibility Condition -μΔu 0 - (λ + μ)⊇ div u 0 + ⊇(Aρ i 0 ) = ρ 1/2 0 g for some radially symmetric g ∈ L 2 . The initial density ρ 0 needs not be positive. We also prove some uniqueness results on the strong solutions.
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unique solvability of the initial boundary value problems for compressible viscous fluids
Journal de Mathématiques Pures et Appliquées, 2004Co-Authors: Yonggeun Cho, Hi Jun Choe, Hyunseok KimAbstract:Abstract We study the Navier–Stokes equations for compressible barotropic fluids in a domain Ω⊂ R 3 . We first prove the local existence of the unique strong solution, provided the initial data satisfy a natural Compatibility Condition. The initial density needs not be bounded away from zero; it may vanish in an open subset (vacuum) of Ω or decay at infinity when Ω is unbounded. We also prove a blow-up criterion for the local strong solution, which is new even for the case of positive initial densities. Finally, we prove that if the initial vacuum is not so irregular, then the Compatibility Condition of the initial data is necessary and sufficient to guarantee the existence of a unique strong solution.
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strong solutions of the navier stokes equations for isentropic compressible fluids
Journal of Differential Equations, 2003Co-Authors: Hi Jun ChoeAbstract:We study strong solutions of the isentropic compressible Navier–Stokes equations in a domain Ω⊂R3. We first prove the local existence of unique strong solutions provided that the initial data ρ0 and u0 satisfy a natural Compatibility Condition. The important point in this paper is that we allow the initial vacuum: the initial density may vanish in an open subset of Ω. We then prove a new uniqueness result and stability result. Our results are valid for unbounded domains as well as bounded ones.
Tao Huang - One of the best experts on this subject based on the ideXlab platform.
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strong solutions of the compressible nematic liquid crystal flow
Journal of Differential Equations, 2012Co-Authors: Tao Huang, Changyou WangAbstract:Abstract We study strong solutions of the simplified Ericksen–Leslie system modeling compressible nematic liquid crystal flows in a domain Ω ⊂ R 3 . We first prove the local existence of a unique strong solution provided that the initial data ρ 0 , u 0 , d 0 are sufficiently regular and satisfy a natural Compatibility Condition. The initial density function ρ 0 may vanish on an open subset (i.e., an initial vacuum may exist). We then prove a criterion for possible breakdown of such a local strong solution at finite time in terms of blow up of the quantities ‖ ρ ‖ L t ∞ L x ∞ and ‖ ∇ d ‖ L t 3 L x ∞ .
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strong solutions of the compressible nematic liquid crystal flow
arXiv: Analysis of PDEs, 2011Co-Authors: Tao Huang, Changyou WangAbstract:We study strong solutions of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in a domain $\Omega \subset\mathbb R^3$. We first prove the local existence of unique strong solutions provided that the initial data $\rho_0, u_0, d_0$are sufficiently regular and satisfy a natural Compatibility Condition. The initial density function $\rho_0$ may vanish on an open subset (i.e., an initial vacuum may exist). We then prove a criterion for possible breakdown of such a local strong solution at finite time in terms of blow up of the quantities $\|\rho\|_{L^\infty_tL^\infty_x}$ and $\|\nabla d\|_{L^3_tL^\infty_x}$.