Universality in mean curvature flow neckpinches

We study noncompact surfaces evolving by mean curvature flow. Without any symmetry assumptions, we prove that any solution that is $C^3$-close at some time to a standard neck will develop a neckpinch singularity in finite time, will become asymptotically rotationally symmetric in a space-time neighborhood of its singular set, and will have a unique tangent flow.Comment: More references added, typos correcte

Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow

We study surfaces evolving by mean curvature flow (MCF). For an open set of initial data that are $C^3$-close to round, but without assuming rotational symmetry or positive mean curvature, we show that MCF solutions become singular in finite time by forming neckpinches, and we obtain detailed asymptotics of that singularity formation. Our results show in a precise way that MCF solutions become asymptotically rotationally symmetric near a neckpinch singularity.Comment: This revision corrects minor but potentially confusing misprints in Section

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Abstract. We study noncompact surfaces evolving by mean curvature flow. Without any symmetry assumptions, we prove that any solution that is C 3-close at some time to a standard neck will develop a neckpinch singularity in finite time, will become asymptotically rotationally symmetric in a space-time neighborhood of its singular set, and will have a unique tangent flow

A New Method for Piecewise Linear Representation of Time Series Data

AbstractIn various methods of modeling of time series, the piecewise linear representation has the advantage of being simple, straightforward and supporting dynamic incremental update of time series. This paper proposed a new method of Piecewise Linear Representation of Time Series based on Slope Change Threshold (SCT). Detailed experiments on real datasets from various fields show that STC representation, compared with several other Piecewise Linear Representations, can be easily calculated and has a high degree of fitting

Identification of the Metabolic Enzyme Involved Morusin Metabolism and Characterization of Its Metabolites by Ultraperformance Liquid Chromatogaphy Quadrupole Time-of-Flight Mass Spectrometry (UPLC/Q-TOF-MS/MS)

Morusin, the important active component of a traditional Chinese medicine, Morus alba L., has been shown to exhibit many vital pharmacological activities. In this study, six recombinant CYP450 supersomes and liver microsomes were used to perform metabolic studies. Chemical inhibition studies and screening assays with recombinant human cytochrome P450s were also used to characterize the CYP450 isoforms involved in morusin metabolism. The morusin metabolites identified varied greatly among different species. Eight metabolites of morusin were detected in the liver microsomes from pigs (PLMs), rats (RLMs), and monkeys (MLMs) by LC-MS/MS and six metabolites were detected in the liver microsomes from humans (HLMs), rabbits (RAMs), and dogs (DLMs). Four metabolites (M1, M2, M5, and M7) were found in all species and hydroxylation was the major metabolic transformation. CYP1A2, CYP2C9, CYP2D6, CYP2E1, CYP3A4, and CYP2C19 contributed differently to the metabolism of morusin. Compared to other CYP450 isoforms, CYP3A4 played the most significant role in the metabolism of morusin in human liver microsomes. These results are significant to better understand the metabolic behaviors of morusin among various species

Gridless Solution Method for Two-Dimensional Unsteady Flow

AbstractThe main purpose of this paper is to develop a gridless method for unsteady flow simulation. A quadrantal point infilling strategy is developed to generate point and combine clouds of points automatically. A point-moving algorithm is introduced to ensure the clouds of points following the movements of body boundaries. A dual time method for solving the two-dimensional Euler equations in Arbitrary Lagrangian-Eulerian (ALE) formulation is presented. Dual time method allows the real-time step to be chosen on the basis of accuracy rather than stability. It also permits the acceleration techniques, which are commonly used to speed up steady flow calculations, to be used when marching the equations in pseudo time. The spatial derivatives, which are used to estimating the inviscid flux, are directly approximated by using local least-squares curve method. An explicit multistage Runge-Kutta algorithm is used to advance the flow equations in pseudo time. In order to accelerate the solution to convergence, local time stepping technique and residual averaging are employed. The results of NACA0012 airfoil in transonic steady flow are presented to verify the accuracy of the present spatial discretization method. Finally, two AGARD standard test cases in which NACA0012 airfoil and NACA64A010 airfoil oscillate in transonic flow are simulated. The computational results are compared with the experimental data to demonstrate the validity and practicality of the presented method