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The Stability Principle and global weak solutions of the free surface semi-geostrophic equations in geostrophic coordinates.

ABSTRACT: The semi-geostrophic equations are used widely in the modelling of large-scale atmospheric flows. In this note, we prove the global existence of weak solutions of the incompressible semi-geostrophic equations, in geostrophic coordinates, in a three-dimensional domain with a free upper boundary. The proof, based on an energy minimization argument originally inspired by the Stability Principle as studied by Cullen, Purser and others, uses optimal transport techniques as well as the analysis of Hamiltonian ODEs in spaces of probability measures as studied by Ambrosio and Gangbo. We also give a general formulation of the Stability Principle in a rigorous mathematical framework.

SUBMITTER: Cullen MJP

PROVIDER: S-EPMC6784401 | biostudies-literature | 2019 Sep

REPOSITORIES: biostudies-literature

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The Stability Principle and global weak solutions of the free surface semi-geostrophic equations in geostrophic coordinates.

Cullen M J P MJP Kuna T T Pelloni B B Wilkinson M M

Proceedings. Mathematical, physical, and engineering sciences 20190904 2229

The semi-geostrophic equations are used widely in the modelling of large-scale atmospheric flows. In this note, we prove the global existence of weak solutions of the incompressible semi-geostrophic equations, in geostrophic coordinates, in a three-dimensional domain with a free upper boundary. The proof, based on an energy minimization argument originally inspired by the Stability Principle as studied by Cullen, Purser and others, uses optimal transport techniques as well as the analysis of Ham ...[more]

PMID: 31611709

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Project description:We present a novel structure determination approach that exploits the global orientational restraints from RDCs to resolve ambiguous NOE assignments. Unlike traditional approaches that bootstrap the initial fold from ambiguous NOE assignments, we start by using RDCs to compute accurate secondary structure element (SSE) backbones at the beginning of structure calculation. Our structure determination package, called RDC-PANDA: (RDC-based SSE PAcking with NOEs for Structure Determination and NOE Assignment), consists of three modules: (1) RDC-EXACT: ; (2) PACKER: ; and (3) HANA: (HAusdorff-based NOE Assignment). RDC-EXACT: computes the global optimal solution of backbone dihedral angles for each secondary structure element by exactly solving a system of quartic RDC equations derived by Wang and Donald (Proceedings of the IEEE computational systems bioinformatics conference (CSB), Stanford, CA, 2004a; J Biomol NMR 29(3):223-242, 2004b), and systematically searching over the roots, each of which is a backbone dihedral varphi- or psi-angle consistent with the RDC data. Using a small number of unambiguous inter-SSE NOEs extracted using only chemical shift information, PACKER: performs a systematic search for the core structure, including all SSE backbone conformations. HANA: uses a Hausdorff-based scoring function to measure the similarity between the experimental spectra and the back-computed NOE pattern for each side-chain from a statistically-diverse rotamer library, and drives the selection of optimal position-specific rotamers for filtering ambiguous NOE assignments. Finally, a local minimization approach is used to compute the loops and refine side-chain conformations by fixing the core structure as a rigid body while allowing movement of loops and side-chains. RDC-PANDA: was applied to NMR data for the FF Domain 2 of human transcription elongation factor CA150 (RNA polymerase II C-terminal domain interacting protein), human ubiquitin, the ubiquitin-binding zinc finger domain of the human Y-family DNA polymerase Eta (pol eta UBZ), and the human Set2-Rpb1 interacting domain (hSRI). These results demonstrated the efficiency and accuracy of our algorithm, and show that RDC-PANDA: can be successfully applied for high-resolution protein structure determination using only a limited set of NMR data by first computing RDC-defined backbones.

Dataset Information

The Stability Principle and global weak solutions of the free surface semi-geostrophic equations in geostrophic coordinates.

Publications

The Stability Principle and global weak solutions of the free surface semi-geostrophic equations in geostrophic coordinates.

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