High order operator splitting methods based on an integral deferred correction framework

Integral deferred correction (IDC) methods have been shown to be an efficient way to achieve arbitrary high order accuracy and possess good stability properties. In this paper, we construct high order operator splitting schemes using the IDC procedure to solve initial value problems (IVPs). We present analysis to show that the IDC methods can correct for both the splitting and numerical errors, lifting the order of accuracy by $r$ with each correction, where $r$ is the order of accuracy of the method used to solve the correction equation. We further apply this framework to solve partial differential equations (PDEs). Numerical examples in two dimensions of linear and nonlinear initial-boundary value problems are presented to demonstrate the performance of the proposed IDC approach.Comment: 33 pages, 22 figure

Positivity-Preserving Finite Difference WENO Schemes with Constrained Transport for Ideal Magnetohydrodynamic Equations

In this paper, we utilize the maximum-principle-preserving flux limiting technique, originally designed for high order weighted essentially non-oscillatory (WENO) methods for scalar hyperbolic conservation laws, to develop a class of high order positivity-preserving finite difference WENO methods for the ideal magnetohydrodynamic (MHD) equations. Our schemes, under the constrained transport (CT) framework, can achieve high order accuracy, a discrete divergence-free condition and positivity of the numerical solution simultaneously. Numerical examples in 1D, 2D and 3D are provided to demonstrate the performance of the proposed method.Comment: 21 pages, 28 figure

High Order Maximum Principle Preserving Semi-Lagrangian Finite Difference WENO schemes for the Vlasov Equation

In this paper, we propose the parametrized maximum principle preserving (MPP) flux limiter, originally developed in [Z. Xu, Math. Comp., (2013), in press], to the semi- Lagrangian finite difference weighted essentially non-oscillatory scheme for solving the Vlasov equation. The MPP flux limiter is proved to maintain up to fourth order accuracy for the semi-Lagrangian finite difference scheme without any time step restriction. Numerical studies on the Vlasov-Poisson system demonstrate the performance of the proposed method and its ability in preserving the positivity of the probability distribution function while maintaining the high order accuracy

Variational models of network formation and ion transport: Applications to perfluorosulfonate ionomer membranes

We present the functionalized Cahn-Hilliard (FCH) energy, a continuum characterization of interfacial energy whose minimizers describe the network morphology of solvated functionalized polymer membranes. With a small set of parameters the FCH characterizes bilayer, pore-like, and micelle network structures. The gradient flows derived from the FCH describe the interactions between these structures, including the merging and pinch-off of endcaps and formation of junctions central to the generation of network morphologies. We couple the FCH gradient flow to a model of ionic transport which incorporates entropic effects to localize counter-ions, yielding a flow which dissipates a total free energy, and an expression for the excess electrochemical potential which combines electrostatic and entropic effects. We present applications to network bifurcation and membrane casting

An explicit high-order single-stage single-step positivity-preserving finite difference WENO method for the compressible Euler equations

In this work we construct a high-order, single-stage, single-step positivity-preserving method for the compressible Euler equations. Space is discretized with the finite difference weighted essentially non-oscillatory (WENO) method. Time is discretized through a Lax-Wendroff procedure that is constructed from the Picard integral formulation (PIF) of the partial differential equation. The method can be viewed as a modified flux approach, where a linear combination of a low- and high-order flux defines the numerical flux used for a single-step update. The coefficients of the linear combination are constructed by solving a simple optimization problem at each time step. The high-order flux itself is constructed through the use of Taylor series and the Cauchy-Kowalewski procedure that incorporates higher-order terms. Numerical results in one- and two-dimensions are presented

Rational Reprogramming of Fungal Polyketide First Ring Cyclization

Resorcylic acid lactones (RAL) and dihydroxyphenylacetic acid lactones (DAL) represent important pharmacophores with heat shock response and immune system modulatory activities. The biosynthesis of these fungal polyketides involves a pair of collaborating iterative polyketide synthases (iPKSs): a highly reducing iPKS (hrPKS) whose product is further elaborated by a nonreducing iPKS (nrPKS) to yield a 1,3-benzenediol moiety bridged by a macrolactone. Biosynthesis of unreduced polyketides requires the sequestration and programmed cyclization of highly reactive poly-β-ketoacyl intermediates to channel these uncommitted, pluripotent substrates towards defined subsets of the polyketide structural space. Catalyzed by product template (PT) domains of the fungal nrPKSs and discrete aromatase/cyclase enzymes in bacteria, regiospecific first-ring aldol cyclizations result in characteristically different polyketide folding modes. However, a few fungal polyketides, including the DAL dehydrocurvularin, derive from a folding event that is analogous to the bacterial folding mode. The structural basis of such a drastic difference in the way a PT domain acts has not been investigated until now. We report here that the fungal versus the bacterial folding mode difference is portable upon creating hybrid enzymes, and structurally characterize the resulting unnatural products. Using structure-guided active site engineering, we unravel structural contributions to regiospecific aldol condensations, and show that reshaping the cyclization chamber of a PT domain by only three selected point mutations is sufficient to reprogram the dehydrocurvularin nrPKS to produce polyketides with a fungal fold. Such rational control of first ring cyclizations will facilitate efforts towards the engineered biosynthesis of novel chemical diversity from natural unreduced polyketides

Linking deeply-sourced volatile emissions to plateau growth dynamics in southeastern Tibetan Plateau

© The Author(s), 2021. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Zhang, M., Guo, Z., Xu, S., Barry, P. H., Sano, Y., Zhang, L., Halldorsson, S. A., Chen, A.-T., Cheng, Z., Liu, C.-Q., Li, S.-L., Lang, Y.-C., Zheng, G., Li, Z., Li, L., & Li, Y. Linking deeply-sourced volatile emissions to plateau growth dynamics in southeastern Tibetan Plateau. Nature Communications, 12(1), (2021): 4157, https://doi.org/10.1038/s41467-021-24415-y.The episodic growth of high-elevation orogenic plateaux is controlled by a series of geodynamic processes. However, determining the underlying mechanisms that drive plateau growth dynamics over geological history and constraining the depths at which growth originates, remains challenging. Here we present He-CO2-N2 systematics of hydrothermal fluids that reveal the existence of a lithospheric-scale fault system in the southeastern Tibetan Plateau, whereby multi-stage plateau growth occurred in the geological past and continues to the present. He isotopes provide unambiguous evidence for the involvement of mantle-scale dynamics in lateral expansion and localized surface uplift of the Tibetan Plateau. The excellent correlation between 3He/4He values and strain rates, along the strike of Indian indentation into Asia, suggests non-uniform distribution of stresses between the plateau boundary and interior, which modulate southeastward growth of the Tibetan Plateau within the context of India-Asia convergence. Our results demonstrate that deeply-sourced volatile geochemistry can be used to constrain deep dynamic processes involved in orogenic plateau growth.This work was supported by China Seismic Experimental Site (CSES) (2019CSES0104), the Strategic Priority Research Program (B) of Chinese Academy of Sciences (XDB26000000), the National Key Research and Development Program of China (2020YFA0607700), the National Natural Science Foundation of China (41930642, 41602341, 41772355, and 41702361), the Second Tibetan Plateau Scientific Expedition and Research Program (STEP) (2019QZKK0702), and the United Laboratory of High-Pressure Physics and Earthquake Science (2019HPPES02). P.H.B. was supported by the US National Science Foundation EAR Grant 1144559 during a portion of this work

Insights into Adaptations to a Near- Obligate Nematode Endoparasitic Lifestyle from the Finished Genome of Drechmeria coniospora

Nematophagous fungi employ three distinct predatory strategies: nematode trapping, parasitism of females and eggs, and endoparasitism. While endoparasites play key roles in controlling nematode populations in nature, their application for integrated pest management is hindered by the limited understanding of their biology. We present a comparative analysis of a high quality finished genome assembly of Drechmeria coniospora, a model endoparasitic nematophagous fungus, integrated with a transcriptomic study. Adaptation of D. coniospora to its almost completely obligate endoparasitic lifestyle led to the simplification of many orthologous gene families involved in the saprophytic trophic mode, while maintaining orthologs of most known fungal pathogen-host interaction proteins, stress response circuits and putative effectors of the small secreted protein type. The need to adhere to and penetrate the host cuticle led to a selective radiation of surface proteins and hydrolytic enzymes. Although the endoparasite has a simplified secondary metabolome, it produces a novel peptaibiotic family that shows antibacterial, antifungal and nematicidal activities. Our analyses emphasize the basic malleability of the D. coniospora genome: loss of genes advantageous for the saprophytic lifestyle; modulation of elements that its cohort species utilize for entomopathogenesis; and expansion of protein families necessary for the nematode endoparasitic lifestyle