Remarks on the asymptotic behavior of scalar auxiliary variable (SAV) schemes for gradient-like flows

We introduce a time semi-discretization of a damped wave equation by a SAV scheme with second order accuracy. The energy dissipation law is shown to hold without any restriction on the time step. We prove that any sequence generated by the scheme converges to a steady state (up to a subsequence). We notice that the steady state equation associated to the SAV scheme is a modified version of the steady state equation associated to the damped wave equation. We show that a similar result holds for a SAV fully discrete version of the Cahn-Hilliard equation and we compare numerically the two steady state equations.     

Purification of Complex of SAV1 with PP1A

SAV1 is a core component involved in the Hippo pathway which can control the organ size via regulating cell proliferation and apoptosis simultaneously. We explored the regulatory mechanism of SAV1. We established the HEK293T cell pool, the cells in which can stably express SAV1 by retroviruses infection and found that SAV1 stable cells reduced the movement of themselves and resulted in multicellular aggregation. We purified SAV1 interacting protein complex using streptavidin resin and subsequently analyzed the digested peptides by high performance liquid chromatography(HPLC)-MS/MS. Results show that about 150 proteins were identified in the complex of SAV1 with protein. TUBA1A, OTUD4, and ATD were identified as proteins interacting with SAV1. Importantly, PP1A, serine/threonine protein phosphatase PP1-alpha 1 catalytic subunit, was also in the top 10 list. The interaction between PP1A and SAV1 was detected by both co-immunoprecipitation(CO-IP) and immunostaining. Our results indicate that PP1A might be the phosphatase of SAV1 and may take part in the regulation of the Hippo pathway.     

A linear energy and entropy-production-rate preserving scheme for thermodynamically consistent crystal growth models

We present a linear, second order, energy and entropy-production-rate preserving scheme for a thermodynamically consistent phase field model for dentritic crystal growth, combining an energy quadratization strategy with the finite element method. The scheme can be decomposed into a series of Poisson equations for efficient numerical implementations. Numerical tests are carried out to verify the accuracy of the scheme and simulations are conducted to demonstrate the effectiveness of the scheme on benchmark examples.     

EFFICIENT LINEAR SCHEMES WITH UNCONDITIONAL ENERGY STABILITY FOR THE PHASE FIELD MODEL OF SOLID-STATE DEWETTING PROBLEMS

In this paper, we study linearly first and second order in time, uniquely solvable and unconditionally energy stable numerical schemes to approximate the phase field model of solid-state dewetting problems based on the novel "scalar auxiliary variable" (SAV) approach, a new developed efficient and accurate method for a large class of gradient flows. The schemes are based on the first order Euler method and the second order backward differential formulas (BDF2) for time discretization, and finite element methods for space discretization. The proposed schemes are proved to be unconditionally stable and the discrete equations are uniquely solvable for all time steps. Various numerical experiments are presented to validate the stability and accuracy of the proposed schemes.