A MIXED FINITE ELEMENT AND CHARACTERISTIC MIXED FINITE ELEMENT FOR INCOMPRESSIBLE MISCIBLE DARCY-FORCHHEIMER DISPLACEMENT AND NUMERICAL ANALYSIS

In this paper a mixed finite element-characteristic mixed finite element method is discussed to simulate an incompressible miscible Darcy-Forchheimer problem.The flow equation is solved by a mixed finite element and the approximation accuracy of Darch-Forchheimer velocity is improved one order.The concentration equation is solved by the method of mixed finite element,where the convection is discretized along the characteristic direction and the diffusion is discretized by the zero-order mixed finite element method.The characteristics can confirm strong stability at sharp fronts and avoids numerical dispersion and nonphysical oscillation.In actual computations the characteristics adopts a large time step without any loss of accuracy.The scalar unknowns and its adjoint vector function are obtained simultaneously and the law of mass conservation holds in every element by the zero-order mixed finite element discretization of diffusion flux.In order to derive the optimal 3/2-order error estimate in L^(2) norm,a post-processing technique is included in the approximation to the scalar unknowns.Numerical experiments are illustrated finally to validate theoretical analysis and efficiency.This method can be used to solve such an important problem.

A Second Order Characteristic Mixed Finite Element Method for Convection Diffusion Reaction Equations

A combined approximate scheme is defined for convection-diffusion-reaction equations. This scheme is constructed by two methods. Standard mixed finite element method is used for diffusion term. A second order characteristic finite element method is presented to handle the material derivative term, that is, the time derivative term plus the convection term. The stability is proved and the L2-norm error estimates are derived for both the scalar unknown variable and its flux. The scheme is of second order accuracy in time increment, symmetric, and unconditionally stable.

Negative regulation of resistance protein-mediated immunity by master transcription factors SARD_1 and CBP60g

Summary Salicylic acid （SA） is an essential defence hormone in plants. Upon pathogen infection, induced biosynthesis of SA is mediated by Isochorismate synthase 1 （ICS1）, whose gene transcription is controlled mainly through two redundant transcription factors, SAR Deficient 1 （SARD0 and Calmodulin- binding protein 6o-like g （CBP60g）.

Redundant CAMTA Transcription Factors Negatively Regulate the Biosynthesis of Salicylic Acid and N-Hydroxypipecolic Acid by Modulating the Expression of SARD1 and CBP60g

Two signal molecules, salicylic acid (SA) and N-hydroxypipecolic acid (NHP), play critical roles in plant immunity. The biosynthetic genes of both compounds are positively regulated by master immune-regulating transcription factors SARD1 and CBP60g. However, the relationship between the SA and NHP pathways is unclear. CALMODULIN-BINDING TRANSCRIPTION FACTOR 1 (CAMTA1), CAMTA2, and CAMTA3 are known redundant negative regulators of plant immunity, but the underlying mechanism also remains largely unknown. In this study, through chromatin immunoprecipitation and electrophoretic mobility shift assays, we uncovered that CBP60g is a direct target of CAMTA3, which also negatively regulates the expression of SARD1, presumably via an indirect effect. The autoimmunity of camta3-1 is suppressed by sard1 cbp60g double mutant as well as ald1 and fmo1, two single mutants defective in NHP biosynthesis. Interestingly, a suppressor screen conducted in the camta1/ 2/ 3 triple mutant background yielded various mutants blocking biosynthesis or signaling of either SA or NHP, leading to nearly complete suppression of the extreme autoimmunity of camta1/ 2/ 3, suggesting that the SA and NHP pathways can mutually amplify each other. Together, these results reveal that CAMTAs repress the biosynthesis of SA and NHP by modulating the expression of SARD1 and CBP60g, and that the SA and NHP pathways are coordinated to optimize plant immune response.

A SPARSE GRID STOCHASTIC COLLOCATION AND FINITE VOLUME ELEMENT METHOD FOR CONSTRAINED OPTIMAL CONTROL PROBLEM GOVERNED BY RANDOM ELLIPTIC EQUATIONS

In this paper, a hybird approximation scheme for an optimal control problem governed by an elliptic equation with random field in its coefficients is considered. The random coefficients are smooth in the physical space and depend on a large number of random variables in the probability space. The necessary and sufficient optimality conditions for the optimal control problem are obtained. The scheme is established to approximate the optimality system through the discretization by using finite volume element method for the spatial space and a sparse grid stochastic collocation method based on the Smolyak approximation for the probability space, respectively. This scheme naturally leads to the discrete solutions of an uncoupled deterministic problem. The existence and uniqueness of the discrete solutions are proved. A priori error estimates are derived for the state, the co-state and the control variables. Numerical examples are presented to illustrate our theoretical results.