The Experts below are selected from a list of 8277 Experts worldwide ranked by ideXlab platform
Pep Espanol - One of the best experts on this subject based on the ideXlab platform.
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non local viscosity from the green kubo formula
Journal of Chemical Physics, 2020Co-Authors: D Duquezumajo, J A De La Torre, Pep EspanolAbstract:We study through MD simulations the correlation matrix of the discrete transverse momentum density field in real space for an unconfined Lennard-Jones fluid at equilibrium. Mori theory predicts this correlation under the Markovian approximation from the knowledge of the non-local shear viscosity matrix, which is given in terms of a Green-Kubo formula. However, the running Green-Kubo integral for the non-local shear viscosity does not have a Plateau. By using a recently proposed correction for the Green-Kubo formula that eliminates the Plateau Problem [Espanol et al., Phys. Rev. E 99, 022126 (2019)], we unambiguously obtain the actual non-local shear viscosity. The resulting Markovian equation, being local in time, is not valid for very short times. We observe that the Markovian equation with non-local viscosity gives excellent predictions for the correlation matrix from a time at which the correlation is around 80% of its initial value. A local in space approximation for the viscosity gives accurate results only after the correlation has decayed to 40% of its initial value.
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microscopic slip boundary conditions in unsteady fluid flows
Physical Review Letters, 2019Co-Authors: J A De La Torre, D Duquezumajo, Diego Camargo, Pep EspanolAbstract:An algebraic tail in the Green-Kubo integral for the solid-fluid friction coefficient hampers its use in the determination of the slip length. A simple theory for discrete nonlocal hydrodynamics near parallel solid walls with extended friction forces is given. We explain the origin of the algebraic tail and give a solution of the Plateau Problem in the Green-Kubo expressions. We derive the slip boundary condition with a microscopic expression for the slip length and the hydrodynamic wall position, and assess it through simulations of an unsteady plug flow.
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solution to the Plateau Problem in the green kubo formula
Physical Review E, 2019Co-Authors: Pep Espanol, J A De La Torre, D DuquezumajoAbstract:Transport coefficients appearing in Markovian dynamic equations for coarse-grained variables have microscopic expressions given by Green-Kubo formulas. These formulas may suffer from the well-known Plateau Problem. The Problem arises because the Green-Kubo running integrals decay as the correlation of the coarse-grained variables themselves. The usual solution is to resort to an extreme timescale separation, for which the Plateau Problem is minor. Within the context of Mori projection operator formulation, we offer an alternative expression for the transport coefficients that is given by a corrected Green-Kubo expression that has no Plateau Problem by construction. The only assumption is that the Markovian approximation is valid in such a way that transport coefficients can be defined, even in the case that the separation of timescales is not extreme.
Wanke Yin - One of the best experts on this subject based on the ideXlab platform.
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flattening of cr singular points and analyticity of the local hull of holomorphy ii
Advances in Mathematics, 2017Co-Authors: Xiaojun Huang, Wanke YinAbstract:Abstract This is the second article of the two papers, in which we investigate the holomorphic and formal flattening Problem of a non-degenerate CR singular point of a codimension two real submanifold in C n with n ≥ 3 . The Problem is motivated from the study of the complex Plateau Problem that looks for the Levi-flat hypersurface bounded by a given real submanifold and by the classical complex analysis Problem of finding the local hull of holomorphy of a real submanifold in a complex space. The present article is focused on non-degenerate flat CR singular points with at least one non-parabolic Bishop invariant. We will solve the formal flattening Problem in this setting. The results in this paper and those in [23] are taken from our earlier arxiv post [22] . We split [22] into two independent articles to avoid it being too long.
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flattening of cr singular points and analyticity of the local hull of holomorphy i
Mathematische Annalen, 2016Co-Authors: Xiaojun Huang, Wanke YinAbstract:This is the first article of the two papers in which we investigate the holomorphic and formal flattening Problem for a codimension two real submanifold in $${\mathbb C}^n$$ with $$n\ge 3$$ near a non-degenerate CR singular point. The Problem is motivated from the study of the complex Plateau Problem that seeks for the Levi-flat hypersurface bounded by a given real submanifold and is motivated by the classical complex analysis Problem of finding the local hull of holomorphy of a real submanifold in a complex space. The present article is focused on the case of CR singular points with at least one elliptic direction. We solve the holomorphic flattening Problem and thus provide a complete description of the local hull of holomorphy in this setting. The results in this paper and those in (Flattening of CR singular points and analyticity of the local hull of holomorphy II, p. 60, 2014) are taken from our arxiv post (Flattening of CR singular points and analyticity of the local hull of holomorphy, 2012). We split (Flattening of CR singular points and analyticity of the local hull of holomorphy, 2012) into two independent articles to avoid it being too long.
D Duquezumajo - One of the best experts on this subject based on the ideXlab platform.
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non local viscosity from the green kubo formula
Journal of Chemical Physics, 2020Co-Authors: D Duquezumajo, J A De La Torre, Pep EspanolAbstract:We study through MD simulations the correlation matrix of the discrete transverse momentum density field in real space for an unconfined Lennard-Jones fluid at equilibrium. Mori theory predicts this correlation under the Markovian approximation from the knowledge of the non-local shear viscosity matrix, which is given in terms of a Green-Kubo formula. However, the running Green-Kubo integral for the non-local shear viscosity does not have a Plateau. By using a recently proposed correction for the Green-Kubo formula that eliminates the Plateau Problem [Espanol et al., Phys. Rev. E 99, 022126 (2019)], we unambiguously obtain the actual non-local shear viscosity. The resulting Markovian equation, being local in time, is not valid for very short times. We observe that the Markovian equation with non-local viscosity gives excellent predictions for the correlation matrix from a time at which the correlation is around 80% of its initial value. A local in space approximation for the viscosity gives accurate results only after the correlation has decayed to 40% of its initial value.
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microscopic slip boundary conditions in unsteady fluid flows
Physical Review Letters, 2019Co-Authors: J A De La Torre, D Duquezumajo, Diego Camargo, Pep EspanolAbstract:An algebraic tail in the Green-Kubo integral for the solid-fluid friction coefficient hampers its use in the determination of the slip length. A simple theory for discrete nonlocal hydrodynamics near parallel solid walls with extended friction forces is given. We explain the origin of the algebraic tail and give a solution of the Plateau Problem in the Green-Kubo expressions. We derive the slip boundary condition with a microscopic expression for the slip length and the hydrodynamic wall position, and assess it through simulations of an unsteady plug flow.
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solution to the Plateau Problem in the green kubo formula
Physical Review E, 2019Co-Authors: Pep Espanol, J A De La Torre, D DuquezumajoAbstract:Transport coefficients appearing in Markovian dynamic equations for coarse-grained variables have microscopic expressions given by Green-Kubo formulas. These formulas may suffer from the well-known Plateau Problem. The Problem arises because the Green-Kubo running integrals decay as the correlation of the coarse-grained variables themselves. The usual solution is to resort to an extreme timescale separation, for which the Plateau Problem is minor. Within the context of Mori projection operator formulation, we offer an alternative expression for the transport coefficients that is given by a corrected Green-Kubo expression that has no Plateau Problem by construction. The only assumption is that the Markovian approximation is valid in such a way that transport coefficients can be defined, even in the case that the separation of timescales is not extreme.
Tristan Riviere - One of the best experts on this subject based on the ideXlab platform.
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the resolution of the yang mills Plateau Problem in super critical dimensions
Advances in Mathematics, 2017Co-Authors: Mircea Petrache, Tristan RiviereAbstract:Abstract We study the minimization Problem for the Yang–Mills energy under fixed boundary connection in supercritical dimension n ≥ 5 . We define the natural function space A G in which to formulate this Problem in analogy to the space of integral currents used for the classical Plateau Problem. The space A G can be also interpreted as a space of weak connections on a “real measure theoretic version” of reflexive sheaves from complex geometry. We prove the existence of weak solutions to the Yang–Mills Plateau Problem in the space A G . We then prove the optimal regularity result for solutions of this Plateau Problem. On the way to prove this result we establish a Coulomb gauge extraction theorem for weak curvatures with small Yang–Mills density. This generalizes to the general framework of weak L 2 curvatures previous works of Meyer–Riviere and Tao–Tian in which respectively a strong approximability property and an admissibility property were assumed in addition.
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immersed spheres of finite total curvature into manifolds
Advances in Calculus of Variations, 2014Co-Authors: Andrea Mondino, Tristan RiviereAbstract:We prove that a sequence of possibly branched, weak immersions of the two-sphere S 2 into an arbitrary compact riemannian manifold (M m ,h) with uniformly bounded area and uniformly bounded L 2 −norm of the second fundamental form either collapse to a point or weakly converges as current, modulo extraction of a subsequence, to a Lipschitz mapping of S 2 and whose image is made of a connected union of finitely many, possibly branched, weak immersions of S 2 with finite total curvature. We prove moreover that if the sequence belongs to a class γ of π2(M m ) the limiting lipschitz mapping of S 2 realizes this class as well. Math. Class. 30C70, 58E15, 58E30, 49Q10, 53A30, 35R01, 35J35, 35J48, 35J50. I Introduction Througout the paper (M m ,h) denotes a connected riemannian manifold and for any x0 ∈ M m we denote respectively by π2(M m ,x0) the homotopy groups of based maps form S 2 into M m sending the south pole to x0 and by π0(C 0 (S 2 ,M m )) the free homotopy classes. It is well known that the group π2(M m ,x0) for different x0's are isomorphic to each other and π2(M) denotes any of the π2(M m ,x0) modulo isomorphisms. Following the classical approach of Douglas and Rado for the Plateau Problem, Sacks and Uhlenbeck proceeded to the minimization of the Dirichlet energy among mappings ~ of the two sphere S 2 into M m
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the resolution of the yang mills Plateau Problem in super critical dimensions
arXiv: Differential Geometry, 2013Co-Authors: Mircea Petrache, Tristan RiviereAbstract:We study the minimization Problem for the Yang-Mills energy under fixed boundary connection in supercritical dimension $n\geq 5$. We define the natural function space A_{G} in which to formulate this Problem in analogy to the space of integral currents used for the classical Plateau Problem. The space A_{G} can be also interpreted as a space of weak connections on a "real measure theoretic version" of reflexive sheaves from complex geometry. We prove the weak closure result which ensures the existence of energy-minimizing weak connections in A_{G}. We then prove that any weak connection from A_{G} can be obtained as a L^2-limit of classical connections over bundles with defects. This approximation result is then extended to a Morrey analogue. We prove the optimal regularity result for Yang-Mills local minimizers. On the way to prove this result we establish a Coulomb gauge extraction theorem for weak curvatures with small Yang-Mills density. This generalizes to the general framework of weak $L^2$ curvatures previous works of Meyer-Riviere and Tao-Tian in which respectively a strong approximability property and an admissibility property were assumed in addition.
Xiaojun Huang - One of the best experts on this subject based on the ideXlab platform.
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flattening a non degenerate cr singular point of real codimension two
Geometric and Functional Analysis, 2018Co-Authors: Hanlong Fang, Xiaojun HuangAbstract:This paper continues the previous studies in two papers of Huang–Yin [HY16,HY17] on the flattening Problem of a CR singular point of real codimension two sitting in a submanifold in $${{\mathbb {C}}^{n+1}}$$ with n + 1 ≥ 3, whose CR points are non-minimal. Partially based on the geometric approach initiated in [HY16] and a formal theory approach used in [HY17], we are able to provide more or less a complete solution to the flattening Problem for a non-degenerate CR singular point along the lines of such studies. As an application, we provide a solution to the local complex Plateau Problem and obtain the analyticity of the local hull of holomorphy near a real analytic definite CR singular point in a general setting.
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flattening a non degenerate cr singular point of real codimension two
arXiv: Complex Variables, 2017Co-Authors: Hanlong Fang, Xiaojun HuangAbstract:This paper continues the previous studies in two papers of Huang-Yin [HY3-4] on the flattening Problem of a CR singular point of real codimension two sitting in a submanifold in ${\mathbb C}^{n+1}$ with $n+1\ge 3$, whose CR points are non-minimal. Partially based on the geometric approach initiated in [HY3] and a formal theory approach used in [HY4], we are able to provide a very general flattening theorem for a non-degenerate CR singular point. As an application, we provide a solution to the local complex Plateau Problem and obtain the analyticity of the local hull of holomorphy near a real analytic definite CR singular point in a general setting.
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flattening of cr singular points and analyticity of the local hull of holomorphy ii
Advances in Mathematics, 2017Co-Authors: Xiaojun Huang, Wanke YinAbstract:Abstract This is the second article of the two papers, in which we investigate the holomorphic and formal flattening Problem of a non-degenerate CR singular point of a codimension two real submanifold in C n with n ≥ 3 . The Problem is motivated from the study of the complex Plateau Problem that looks for the Levi-flat hypersurface bounded by a given real submanifold and by the classical complex analysis Problem of finding the local hull of holomorphy of a real submanifold in a complex space. The present article is focused on non-degenerate flat CR singular points with at least one non-parabolic Bishop invariant. We will solve the formal flattening Problem in this setting. The results in this paper and those in [23] are taken from our earlier arxiv post [22] . We split [22] into two independent articles to avoid it being too long.
-
flattening of cr singular points and analyticity of the local hull of holomorphy i
Mathematische Annalen, 2016Co-Authors: Xiaojun Huang, Wanke YinAbstract:This is the first article of the two papers in which we investigate the holomorphic and formal flattening Problem for a codimension two real submanifold in $${\mathbb C}^n$$ with $$n\ge 3$$ near a non-degenerate CR singular point. The Problem is motivated from the study of the complex Plateau Problem that seeks for the Levi-flat hypersurface bounded by a given real submanifold and is motivated by the classical complex analysis Problem of finding the local hull of holomorphy of a real submanifold in a complex space. The present article is focused on the case of CR singular points with at least one elliptic direction. We solve the holomorphic flattening Problem and thus provide a complete description of the local hull of holomorphy in this setting. The results in this paper and those in (Flattening of CR singular points and analyticity of the local hull of holomorphy II, p. 60, 2014) are taken from our arxiv post (Flattening of CR singular points and analyticity of the local hull of holomorphy, 2012). We split (Flattening of CR singular points and analyticity of the local hull of holomorphy, 2012) into two independent articles to avoid it being too long.