This paper provides theoretical justification that Anderson acceleration (AA) improves the convergence rate of contractive fixed-point iterations in vicinity a fixed-point. AA has been used for decades to speed up nonlinear solvers many applications. However, rigorous mathematical improved remained lacking. The key ideas analysis presented here are relating difference consecutive iterates residuals based on performing inner-optimization Hilbert space setting, and explicitly defining gain...

Vesicles and membrane properties play critical roles in reproducing the natural environment of living cells such as nutrient transport DNA protection. We report how to control morphology evolutionary stages self-assembly amphiphilic block copolymers composed hydrophilic–hydrophobic–hydrophilic structure using dissipative particle dynamics method. Two unique intermediate states are obtained by controlling hydrophobic/hydrophilic ratio, polymer–solvent interaction, polymer concentration: (1)...

We propose, analyze, and test Anderson-accelerated Picard iterations for solving the incompressible Navier--Stokes equations (NSE). Anderson acceleration has recently gained interest as a strategy to accelerate linear nonlinear iterations, based on including an optimization step in each iteration. extend theory steady NSE setting prove that improves convergence rate of iteration success underlying problem. The is demonstrated several numerical tests, with particularly marked improvement...

The Newton's method for solving stationary Navier-Stokes equations (NSE) is known to convergent fast, however, may fail due a bad initial guess. This work presents simple-to-implement nonlinear preconditioning of iteration, that remains the quadratic convergence and enlarges domain convergence. proposed AAPicard-Newton adds Anderson accelerated Picard step at each iteration NSE, which has been shown globally stable relaxation parameter $\beta_{k+1}\equiv1$ in acceleration optimization step,...

Computer-aided diagnosis technology based on the deep learning greatly increases efficiency of medical tasks. However, black-box nature neural networks reduces reliability auxiliary clinical diagnosis, so it is necessary to explain imaging model learning. The Gradient-weighted Class Activation Mapping (Grad-CAM) can determine contribution input features result classification task and visualize these contributions as heatmaps. due structural difference between segmentation model, Grad-CAM...

Our recent simulation study on mechanisms of vesicle formation in ABA triblock copolymer system has revealed the factors or conditions that lead to transition from mechanism I (a bilayer membrane closing pathway) II nucleation and growth pathway). The spontaneous involves many metastable states two do not each a unique intermediate structure, but have period. In this paper, we use dissipative particle dynamics (DPD) simulations further investigate effect size hydrophobicity blocks...

The spontaneous vesicle formation of ABABA-type amphiphilic multiblock copolymers bearing thermosensitive hydrophilic A-block in a selective solvent is studied using dissipative particle dynamics (DPD) approach. process through nucleation and growth pathway observed by varying the temperature. simulation results show that spherical micelle takes shape at high As temperature decreases, vesicles with small aqueous cavity appear expands as well membrane thickness decreases further decreasing....

Localization of nanoparticles in assemblies amphiphilic diblock copolymers can be controlled by varying the immiscibility and copolymers.

This paper studies a new alteration of Yosida algebraic splitting methods for the Navier--Stokes equations. By applying usual or pressure-corrected techniques to discretizations written in terms velocity and pressure updates $(u^{n+1}-u^n,p^{n+1}-p^n)$, we show that accuracy is increased by one full order $\Delta t$ without any additional cost respective methods. Proofs convergence results are given both linear finite element frameworks. Several numerical tests which reveal (sometimes...

Abstract This article studies the performance Newton's iteration applied with Anderson acceleration for solving incompressible steady Navier–Stokes equations. We manifest that this method converges superlinearly a good initial guess, and moreover, large depth decelerates convergence speed comparing to small depth. observe numerical tests confirm these analytical results, in addition, sometimes enlarges domain of method.

The translocation process of star polymers through a nanochannel is investigated by dissipative particle dynamics simulations. strongly influenced the arm arrangement as polymer enters channel, and scaling relation between time τ total number beads Ntot obtained. Qualitative agreements are found with predictions nucleation growth model for linear block co-polymer translocation. In intermediate stage where center at channel entrance, to have power law-dependence on arms outside very weakly...

Abstract This paper develops an efficient and robust solution technique for the steady Boussinesq model of non-isothermal flow using Anderson acceleration applied to a Picard iteration. After analyzing fixed point operator associated with nonlinear iteration prove that certain stability regularity properties hold, we apply authors’ recently constructed theory acceleration, which yields convergence result accelerated system. The shows leading term in residual is improved by gain optimization...

The oxidation of amitriptyline (AMI) and nortriptyline (NOR), two typical tricyclic antidepressants, has been studied in ferrate(VI) (Fe(VI)) solution. removal rate AMI NOR increased with increasing Fe(VI) dosage was seen to be pH dependent the order 7.0 < 10.0 8.0 9.0. UV irradiation at 254 nm found exert a synergistic effect on NOR. By LC–ESI-MS/MS analysis, main products by have identified. exocyclic double bond is first oxidized give exo-epoxide, which then hydrolyzed finally...

We report a new three-dimensional ab initio intermolecular potential energy surface for the Ne-H(2)S complex with H(2)S monomer fixed at its experimental average structure. Using supermolecular approach, energies were evaluated CCSD(T) (coupled cluster single and double perturbative triple excitations) level large basis sets including bond functions. The full counterpoise procedure was employed to correct set superposition error. planar T-shaped global minimum is located distance of 3.51 Å...

Objective: To investigate the relationship between shift work and overweight/obesity in male steel workers. Methods: A questionnaire survey was conducted among workers selected during health examination Tangshan Steel Company from March 2015 to 2016. The were analyzed by using logistic regression model restricted cubic splinemodel. Results: total of 7 262 surveyed, overall prevalence overweight/obesitywas 64.5% (4 686/7 262), overweight rate 34.3% obesity 30.2%, respectively. After adjusting...

We propose new, efficient, and simple nonlinear iteration methods for the incompressible Navier-Stokes equations. The are constructed by applying Yosida-type algebraic splitting to linear systems that arise from grad-div stabilized finite element implementations of incremental Picard Newton iterations. They efficient because at each iteration, same symmetric positive definite Schur complement system needs be solved, which allows CG used inner outer solvers, preconditioning, reusing...

The incremental Picard Yosida (IPY) method has recently been developed as an iteration for nonlinear saddle point problems that is effective but more efficient. By combining ideas from algebraic splitting of linear solvers with Picard‐type iterations and grad‐div stabilization, IPY improves on the standard by allowing easier solves at each iteration—but without creating total compared to Picard. This paper extends methodology studying it together Anderson acceleration (AA). We prove...

This paper provides the first proof that Anderson acceleration (AA) improves convergence rate of general fixed point iterations. AA has been used for decades to speed up nonlinear solvers in many applications, however a rigorous mathematical justification improved remained lacking. The key ideas analysis presented here are relating difference consecutive iterates residuals based on performing inner-optimization Hilbert space setting, and explicitly defining gain optimization stage be ratio...