The Experts below are selected from a list of 63 Experts worldwide ranked by ideXlab platform
Pengzi Miao - One of the best experts on this subject based on the ideXlab platform.
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On Existence of Static Metric Extensions in General Relativity
Communications in Mathematical Physics, 2003Co-Authors: Pengzi MiaoAbstract:Motivated by problems related to quasi-local mass in general relativity, we study the static metric extension conjecture proposed by R. Bartnik [4]. We show that, for any metric on ¯ B _1 that is close enough to the Euclidean metric and has reflection invariant Boundary data, there always exists an asymptotically flat and scalar flat static metric extension in M =ℝ^3∖ B _1 such that it satisfies Bartnik's Geometric Boundary Condition [4] on ∂ B _1.
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Variational Effect of Boundary Mean Curvature on ADM Mass in General Relativity
arXiv: Mathematical Physics, 2003Co-Authors: Pengzi MiaoAbstract:We extend the idea and techniques in \cite{Miao} to study variational effect of the Boundary geometry on the ADM mass of an asymptotically flat manifold. We show that, for a Lipschitz asymptotically flat metric extension of a bounded Riemannian domain with quasi-convex Boundary, if the Boundary mean curvature of the extension is dominated by but not identically equal to the one determined by the given domain, we can decrease its ADM mass while raising its Boundary mean curvature. Thus our analysis implies that, for a domain with quasi-convex Boundary, the Geometric Boundary Condition holds in Bartnik's minimal mass extension conjecture \cite{Bartnik_energy}.
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On Existence of Static Metric Extensions in General Relativity
Communications in Mathematical Physics, 2003Co-Authors: Pengzi MiaoAbstract:Motivated by problems related to quasi-local mass in general relativity, we study the static metric extension conjecture proposed by R. Bartnik \cite{Bartnik_energy}. We show that, for any metric on $\bar{B}_1$ that is close enough to the Euclidean metric and has reflection invariant Boundary data, there always exists an asymptotically flat and scalar flat {\em static} metric extension in $M = \R^3 \setminus B_1$ such that it satisfies Bartnik's Geometric Boundary Condition \cite{Bartnik_energy} on $\partial B_1$.
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positive mass theorem on manifolds admitting corners along a hypersurface
arXiv: Mathematical Physics, 2002Co-Authors: Pengzi MiaoAbstract:We study a class of non-smooth asymptotically flat manifolds on which metrics fails to be $C^1$ across a hypersurface $\Sigma$. We first give an approximation scheme to mollify the metric, then we prove that the Positive Mass Theorem still holds on these manifolds if a Geometric Boundary Condition is satisfied by metrics separated by $\Sigma$.
Yusuke T. Maeda - One of the best experts on this subject based on the ideXlab platform.
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Geometry-driven collective ordering of bacterial vortices
Soft matter, 2017Co-Authors: Kazusa Beppu, Ziane Izri, Jun Gohya, Kanta Eto, Masatoshi Ichikawa, Yusuke T. MaedaAbstract:Controlling the phases of matter is a challenge that spans from condensed materials to biological systems. Here, by imposing a Geometric Boundary Condition, we study controlled collective motion of Escherichia coli bacteria. A circular microwell isolates a rectified vortex from disordered vortices masked in bulk. For a doublet of microwells, two vortices emerge but their spinning directions show transition from parallel to anti-parallel. A Vicsek-like model for confined self-propelled particles gives the point where two spinning patterns occur in equal probability and one Geometric quantity governs the transition as seen in experiments. This mechanism shapes rich patterns including chiral configurations in a quadruplet of microwells, thus revealing a design principle of active vortices.
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Geometry-driven collective ordering of bacterial vortices
2017Co-Authors: Kazusa Beppu, Ziane Izri, Jun Gohya, Kanta Eto, Masatoshi Ichikawa, Yusuke T. MaedaAbstract:Controlling the phases of matter is a challenge that spans from condensed materials to biological systems. Here, by imposing a Geometric Boundary Condition, we study the controlled collective motion of Escherichia coli bacteria. A circular microwell isolates a rectified vortex from disordered vortices masked in the bulk. For a doublet of microwells, two vortices emerge but their spinning directions show transition from parallel to anti-parallel. A Vicsek-like model for confined self-propelled particles gives the point where the two spinning patterns occur in equal probability and one Geometric quantity governs the transition as seen in experiments. This mechanism shapes rich patterns including chiral configurations in a quadruplet of microwells, thus revealing a design principle of active vortices.
Kazusa Beppu - One of the best experts on this subject based on the ideXlab platform.
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Geometry-driven collective ordering of bacterial vortices
Soft matter, 2017Co-Authors: Kazusa Beppu, Ziane Izri, Jun Gohya, Kanta Eto, Masatoshi Ichikawa, Yusuke T. MaedaAbstract:Controlling the phases of matter is a challenge that spans from condensed materials to biological systems. Here, by imposing a Geometric Boundary Condition, we study controlled collective motion of Escherichia coli bacteria. A circular microwell isolates a rectified vortex from disordered vortices masked in bulk. For a doublet of microwells, two vortices emerge but their spinning directions show transition from parallel to anti-parallel. A Vicsek-like model for confined self-propelled particles gives the point where two spinning patterns occur in equal probability and one Geometric quantity governs the transition as seen in experiments. This mechanism shapes rich patterns including chiral configurations in a quadruplet of microwells, thus revealing a design principle of active vortices.
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Geometry-driven collective ordering of bacterial vortices
2017Co-Authors: Kazusa Beppu, Ziane Izri, Jun Gohya, Kanta Eto, Masatoshi Ichikawa, Yusuke T. MaedaAbstract:Controlling the phases of matter is a challenge that spans from condensed materials to biological systems. Here, by imposing a Geometric Boundary Condition, we study the controlled collective motion of Escherichia coli bacteria. A circular microwell isolates a rectified vortex from disordered vortices masked in the bulk. For a doublet of microwells, two vortices emerge but their spinning directions show transition from parallel to anti-parallel. A Vicsek-like model for confined self-propelled particles gives the point where the two spinning patterns occur in equal probability and one Geometric quantity governs the transition as seen in experiments. This mechanism shapes rich patterns including chiral configurations in a quadruplet of microwells, thus revealing a design principle of active vortices.
Masatoshi Ichikawa - One of the best experts on this subject based on the ideXlab platform.
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Geometry-driven collective ordering of bacterial vortices
Soft matter, 2017Co-Authors: Kazusa Beppu, Ziane Izri, Jun Gohya, Kanta Eto, Masatoshi Ichikawa, Yusuke T. MaedaAbstract:Controlling the phases of matter is a challenge that spans from condensed materials to biological systems. Here, by imposing a Geometric Boundary Condition, we study controlled collective motion of Escherichia coli bacteria. A circular microwell isolates a rectified vortex from disordered vortices masked in bulk. For a doublet of microwells, two vortices emerge but their spinning directions show transition from parallel to anti-parallel. A Vicsek-like model for confined self-propelled particles gives the point where two spinning patterns occur in equal probability and one Geometric quantity governs the transition as seen in experiments. This mechanism shapes rich patterns including chiral configurations in a quadruplet of microwells, thus revealing a design principle of active vortices.
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Geometry-driven collective ordering of bacterial vortices
2017Co-Authors: Kazusa Beppu, Ziane Izri, Jun Gohya, Kanta Eto, Masatoshi Ichikawa, Yusuke T. MaedaAbstract:Controlling the phases of matter is a challenge that spans from condensed materials to biological systems. Here, by imposing a Geometric Boundary Condition, we study the controlled collective motion of Escherichia coli bacteria. A circular microwell isolates a rectified vortex from disordered vortices masked in the bulk. For a doublet of microwells, two vortices emerge but their spinning directions show transition from parallel to anti-parallel. A Vicsek-like model for confined self-propelled particles gives the point where the two spinning patterns occur in equal probability and one Geometric quantity governs the transition as seen in experiments. This mechanism shapes rich patterns including chiral configurations in a quadruplet of microwells, thus revealing a design principle of active vortices.
Kanta Eto - One of the best experts on this subject based on the ideXlab platform.
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Geometry-driven collective ordering of bacterial vortices
Soft matter, 2017Co-Authors: Kazusa Beppu, Ziane Izri, Jun Gohya, Kanta Eto, Masatoshi Ichikawa, Yusuke T. MaedaAbstract:Controlling the phases of matter is a challenge that spans from condensed materials to biological systems. Here, by imposing a Geometric Boundary Condition, we study controlled collective motion of Escherichia coli bacteria. A circular microwell isolates a rectified vortex from disordered vortices masked in bulk. For a doublet of microwells, two vortices emerge but their spinning directions show transition from parallel to anti-parallel. A Vicsek-like model for confined self-propelled particles gives the point where two spinning patterns occur in equal probability and one Geometric quantity governs the transition as seen in experiments. This mechanism shapes rich patterns including chiral configurations in a quadruplet of microwells, thus revealing a design principle of active vortices.
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Geometry-driven collective ordering of bacterial vortices
2017Co-Authors: Kazusa Beppu, Ziane Izri, Jun Gohya, Kanta Eto, Masatoshi Ichikawa, Yusuke T. MaedaAbstract:Controlling the phases of matter is a challenge that spans from condensed materials to biological systems. Here, by imposing a Geometric Boundary Condition, we study the controlled collective motion of Escherichia coli bacteria. A circular microwell isolates a rectified vortex from disordered vortices masked in the bulk. For a doublet of microwells, two vortices emerge but their spinning directions show transition from parallel to anti-parallel. A Vicsek-like model for confined self-propelled particles gives the point where the two spinning patterns occur in equal probability and one Geometric quantity governs the transition as seen in experiments. This mechanism shapes rich patterns including chiral configurations in a quadruplet of microwells, thus revealing a design principle of active vortices.