Parameter estimation for a morphochemical reaction-diffusion model of electrochemical pattern formation

The process of electrodeposition can be described in terms of a reaction-diffusion partial differential equation (PDE) system that models the dynamics of the morphology profile and the chemical composition. Here we fit such a model to the different patterns present in a range of electrodeposited and electrochemically modified alloys using PDE constrained optimization. Experiments with simulated data show how the parameter space of the model can be divided into zones corresponding to the different physical patterns by examining the structure of an appropriate cost function. We then use real data to demonstrate how numerical optimization of the cost function can allow the model to fit the rich variety of patterns arising in experiments. The computational technique developed provides a potential tool for tuning experimental parameters to produce desired patterns.     

Low‐order optimal regulation of parabolic PDEs with time‐dependent domain

Observer and optimal boundary control design for the objective of output tracking of a linear distributed parameter system given by a two‐dimensional (2‐D) parabolic partial differential equation with time‐varying domain is realized in this work. The transformation of boundary actuation to distributed control setting allows to represent the system's model in a standard evolutionary form. By exploring dynamical model evolution and generating data, a set of time‐varying empirical eigenfunctions that capture the dominant dynamics of the distributed system is found. This basis is used in Galerkin's method to accurately represent the distributed system as a finite‐dimensional plant in terms of a linear time‐varying system. This reduced‐order model enables synthesis of a linear optimal output tracking controller, as well as design of a state observer. Finally, numerical results are prepared for the optimal output tracking of a 2‐D model of the temperature distribution in Czochralski crystal growth process which has nontrivial geometry. © 2014 American Institute of Chemical Engineers AIChE J, 61: 494–502, 2015     

Development of Phosphodiesterase–Protein-Kinase Complexes as Novel Targets for Discovery of Inhibitors with Enhanced Specificity

Phosphodiesterases (PDEs) hydrolyze cyclic nucleotides to modulate multiple signaling events in cells. PDEs are recognized to actively associate with cyclic nucleotide receptors (protein kinases, PKs) in larger macromolecular assemblies referred to as signalosomes. Complexation of PDEs with PKs generates an expanded active site that enhances PDE activity. This facilitates signalosome-associated PDEs to preferentially catalyze active hydrolysis of cyclic nucleotides bound to PKs and aid in signal termination. PDEs are important drug targets, and current strategies for inhibitor discovery are based entirely on targeting conserved PDE catalytic domains. This often results in inhibitors with cross-reactivity amongst closely related PDEs and attendant unwanted side effects. Here, our approach targeted PDE–PK complexes as they would occur in signalosomes, thereby offering greater specificity. Our developed fluorescence polarization assay was adapted to identify inhibitors that block cyclic nucleotide pockets in PDE–PK complexes in one mode and disrupt protein-protein interactions between PDEs and PKs in a second mode. We tested this approach with three different systems—cAMP-specific PDE8–PKAR, cGMP-specific PDE5–PKG, and dual-specificity RegA–R_D complexes—and ranked inhibitors according to their inhibition potency. Targeting PDE–PK complexes offers biochemical tools for describing the exquisite specificity of cyclic nucleotide signaling networks in cells.     

A residual-free bubble formulation for nonlinear elliptic problems with oscillatory coefficients

We present an investigation of the Residual-Free Bubble (RFB) finite element method for a class of multiscale nonlinear elliptic partial differential equations. After proposing a nonlinear version for the method, we address fundamental questions as existence and uniqueness of solutions. We also obtain a best approximation result and investigate possible linearizations that generate different versions for the method. All estimates are independent of eventual oscillations in the coefficients, and as far as we are aware, this is the first time that an analysis for the nonlinear RFB method is considered.     

Transported snapshot model order reduction approach for parametric,steady-state fluid flows containing parameter-dependent shocks

A new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientations are strongly parameter dependent. In this method, solutions in the predictive regime are approximated using a linear superposition of parameter-dependent basis. The sought-after parametric reduced bases are obtained by transporting the snapshots in a spatially and parametrically dependent transport field. Key to the proposed approach is the observation that the transport fields are typically smooth and continuous, despite the solution themselves not being so. As a result, the transport fields can be accurately expressed using a low-order polynomial expansion. Similar to traditional projection-based model order reduction approaches, the proposed method is formulated mathematically as a residual minimization problem for the generalized coordinates. The proposed approach is also integrated with well-known hyper-reduction strategies to obtain significant computational speedups. The method is successfully applied to the reduction of a parametric one-dimensional flow in a converging-diverging nozzle, a parametric two-dimensional supersonic flow over a forward-facing step, and a parametric two-dimensional jet diffusion flame in a combustor.     

Higher-order Hamilton dynamics and Hamilton–Jacobi divergence PDE

This paper, using a non-standard Legendrian duality, investigates the Hamiltonian dynamics and formulates a Hamilton–Jacobi type divergence PDE governed by higher-order Lagrangians.     

百草枯催吐剂三氮唑嘧啶酮的合成

甲基丙烯酸甲酯经溴化加成、醚化、催化裂化得3-甲氧基-2-甲基丙烯酸甲酯;单氰胺与二硫化碳在碱性条件下缩合、甲基化得氰亚胺基二硫代碳酸二甲酯,后与正丙胺缩合再与水合肼环合得氨基正丙胺基三氮唑,与苯甲醛醛缩合得醛缩物,再在缚酸剂下与3-甲氧基-2-甲基丙烯酸甲酯催化闭环后在盐酸中水解、去醛基得目标物。选择cat1#/2#为裂解和闭环催化剂,反应总收率达55.4%,产品纯度99.5%。     

Proximal schemes for parabolic optimal control problems with sparsity promoting cost functionals

Fast first-order proximal methods that solve linear and bilinear parabolic optimal control problems with a sparsity cost functional are discussed. Weak convergence of these methods is proved and, for benchmarking purposes, the proposed inexact proximal schemes are compared to an inexact semi-smooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectiveness of proximal schemes and to validate the theoretical estimates.     

两点边值问题的区间小波Galerkin方法

用改进后的区间小波，结合反导数方法生成Ｓｏｂｏｌｅｖ空间中的基，使刚度矩阵的条件数有所降低。提出了逐层算法，使得小波Ｇａｌｅｒｋｉｎ法能充分地利用多分辨分析的正交性实现事后误差估计和局部加密。最后通过对两点边值问题的实例计算验证了结论的正确性。     

Averaged control

We analyze the problem of controlling parameter-dependent systems. We introduce the notion of averaged control according to which the quantity of interest is the average of the states with respect to the parameter.First we consider the problem of controllability for linear finite-dimensional systems and show that a necessary and sufficient condition for averaged controllability is an averaged rank condition, in the spirit of the classical rank condition for linear control systems, but involving averaged momenta of any order of the matrices generating the dynamics and representing the control action.We also describe some open problems and directions of possible research, in particular on the average controllability of evolution partial differential equations. In this context we analyze also the averaged version of a classical optimal control problem for a parameter dependent elliptic equation and derive the corresponding optimality system.