Applied Numerical Mathematics最新文献

英文中文

Implicit integration factor method coupled with Padé approximation strategy for nonlocal Allen-Cahn equation

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-03-03 DOI: 10.1016/j.apnum.2025.02.019

Yuxin Zhang , Hengfei Ding

The space nonlocal Allen-Cahn equation is a famous example of fractional reaction-diffusion equations. It is also an extension of the classical Allen-Cahn equation, which is widely used in physics to describe the phenomenon of two-phase fluid flows. Due to the nonlocality of the nonlocal operator, numerical solutions to these equations face considerable challenges. It is worth noting that whether we use low-order or high-order numerical differential formulas to approximate the operator, the corresponding matrix is always dense, which implies that the storage space and computational cost required for the former and the latter are the same. However, the higher-order formula can significantly improve the accuracy of the numerical scheme. Therefore, the primary goal of this paper is to construct a high-order numerical formula that approximates the nonlocal operator. To reduce the time step limitation in existing numerical algorithms, we employed a technique combining the compact integration factor method with the Padé approximation strategy to discretize the time derivative. A novel high-order numerical scheme, which satisfies both the maximum principle and energy stability for the space nonlocal Allen-Cahn equation, is proposed. Furthermore, we provide a detailed error analysis of the differential scheme, which shows that its convergence order is

O (τ^{2} + h^{6})

. Especially, it is worth mentioning that the fully implicit scheme with sixth-order accuracy in spatial has never been proven to maintain the maximum principle and energy stability before. Finally, some numerical experiments are carried out to demonstrate the efficiency of the proposed method.

{"title":"Implicit integration factor method coupled with Padé approximation strategy for nonlocal Allen-Cahn equation","authors":"Yuxin Zhang , Hengfei Ding","doi":"10.1016/j.apnum.2025.02.019","DOIUrl":"10.1016/j.apnum.2025.02.019","url":null,"abstract":"<div><div>The space nonlocal Allen-Cahn equation is a famous example of fractional reaction-diffusion equations. It is also an extension of the classical Allen-Cahn equation, which is widely used in physics to describe the phenomenon of two-phase fluid flows. Due to the nonlocality of the nonlocal operator, numerical solutions to these equations face considerable challenges. It is worth noting that whether we use low-order or high-order numerical differential formulas to approximate the operator, the corresponding matrix is always dense, which implies that the storage space and computational cost required for the former and the latter are the same. However, the higher-order formula can significantly improve the accuracy of the numerical scheme. Therefore, the primary goal of this paper is to construct a high-order numerical formula that approximates the nonlocal operator. To reduce the time step limitation in existing numerical algorithms, we employed a technique combining the compact integration factor method with the Padé approximation strategy to discretize the time derivative. A novel high-order numerical scheme, which satisfies both the maximum principle and energy stability for the space nonlocal Allen-Cahn equation, is proposed. Furthermore, we provide a detailed error analysis of the differential scheme, which shows that its convergence order is <span><math><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>6</mn></mrow></msup><mo>)</mo></mrow></math></span>. Especially, it is worth mentioning that the fully implicit scheme with sixth-order accuracy in spatial has never been proven to maintain the maximum principle and energy stability before. Finally, some numerical experiments are carried out to demonstrate the efficiency of the proposed method.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"213 ","pages":"Pages 88-107"},"PeriodicalIF":2.2,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143548519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Numerical approximations for a hyperbolic integrodifferential equation with a non-positive variable-sign kernel and nonlinear-nonlocal damping

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-02-26 DOI: 10.1016/j.apnum.2025.02.018

Wenlin Qiu , Xiangcheng Zheng , Kassem Mustapha

This work considers the Galerkin approximation and analysis for a hyperbolic integrodifferential equation, where the non-positive variable-sign kernel and nonlinear-nonlocal damping with both the weak and viscous damping effects are involved. We derive the long-time stability of the solution and its finite-time uniqueness. For the semi-discrete-in-space Galerkin scheme, we derive the long-time stability of the semi-discrete numerical solution and its finite-time error estimate by technical splitting of intricate terms. Then we further apply the centering difference method and the interpolating quadrature to construct a fully discrete Galerkin scheme and prove the long-time stability of the numerical solution and its finite-time error estimate by designing a new semi-norm. Numerical experiments are performed to verify the theoretical findings.

引用次数: 0

Well-balanced and positivity-preserving wet-dry front reconstruction scheme for Ripa models

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-02-25 DOI: 10.1016/j.apnum.2025.02.014

Xue Wang , Guoxian Chen

This paper explores the reconstruction of wet-dry fronts (WDF) for solving both one-dimensional (1D) and two-dimensional (2D) Ripa systems, with a particular emphasis on the influence of temperature. Our aim is to develop a well-balanced numerical scheme that not only preserves the steady state but also ensures the positivity of both water height and temperature. By employing conservative variables for reconstruction instead of equilibrium variables, we have achieved a significant doubling of the CFL number for fully flooded cells. We have refined the original 1D WDF reconstruction method and further enhanced the corresponding 2D scheme. The conservation principle and linearity observed in the wet region of partially flooded cells indicate a constant cell-wise velocity and temperature. Additionally, we introduce a novel draining time approach to adjust the numerical flux in an upwind manner, ensuring both stability and efficiency, even for partially flooded cells. Numerical examples are presented to demonstrate the well-balanced property, high-order accuracy, and positivity-preserving characteristics of our proposed method. These examples also showcase the method's ability to capture small perturbations in the lake-at-rest steady state, highlighting its potential for practical applications.

{"title":"Well-balanced and positivity-preserving wet-dry front reconstruction scheme for Ripa models","authors":"Xue Wang , Guoxian Chen","doi":"10.1016/j.apnum.2025.02.014","DOIUrl":"10.1016/j.apnum.2025.02.014","url":null,"abstract":"<div><div>This paper explores the reconstruction of wet-dry fronts (WDF) for solving both one-dimensional (1D) and two-dimensional (2D) Ripa systems, with a particular emphasis on the influence of temperature. Our aim is to develop a well-balanced numerical scheme that not only preserves the steady state but also ensures the positivity of both water height and temperature. By employing conservative variables for reconstruction instead of equilibrium variables, we have achieved a significant doubling of the CFL number for fully flooded cells. We have refined the original 1D WDF reconstruction method and further enhanced the corresponding 2D scheme. The conservation principle and linearity observed in the wet region of partially flooded cells indicate a constant cell-wise velocity and temperature. Additionally, we introduce a novel draining time approach to adjust the numerical flux in an upwind manner, ensuring both stability and efficiency, even for partially flooded cells. Numerical examples are presented to demonstrate the well-balanced property, high-order accuracy, and positivity-preserving characteristics of our proposed method. These examples also showcase the method's ability to capture small perturbations in the lake-at-rest steady state, highlighting its potential for practical applications.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"213 ","pages":"Pages 38-60"},"PeriodicalIF":2.2,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143507961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Drug release from polymeric platforms for non smooth solutions

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-02-25 DOI: 10.1016/j.apnum.2025.02.016

J.S. Borges , G.C.M. Campos , J.A. Ferreira , G. Romanazzi

This paper aims to conclude a sequence of works focused in the numerical study of a system of partial differential equations in a nonuniform grid that can be used to describe the drug release from polymeric platforms. The drug release is a consequence of the non-Fickian fluid uptake, the dissolution process and the Fickian drug transport. The development of a computational tool and its theoretical convergence support was the common driven force. In a previous work from the authors, second order error estimates were established for the numerical approximations for the solvent, solid drug and dissolved drug considering severe smoothness assumption on the solutions: the solvent and the dissolve drug were

C^{4}

- functions. In the present work, our aim is to establish second order estimates for the same variables reducing the smoothness assumption, namely, we assume that the solvent and the dissolved drug are

H^{3}

- functions. Numerical experiments illustrating the obtained theoretical results are also included.

{"title":"Drug release from polymeric platforms for non smooth solutions","authors":"J.S. Borges , G.C.M. Campos , J.A. Ferreira , G. Romanazzi","doi":"10.1016/j.apnum.2025.02.016","DOIUrl":"10.1016/j.apnum.2025.02.016","url":null,"abstract":"<div><div>This paper aims to conclude a sequence of works focused in the numerical study of a system of partial differential equations in a nonuniform grid that can be used to describe the drug release from polymeric platforms. The drug release is a consequence of the non-Fickian fluid uptake, the dissolution process and the Fickian drug transport. The development of a computational tool and its theoretical convergence support was the common driven force. In a previous work from the authors, second order error estimates were established for the numerical approximations for the solvent, solid drug and dissolved drug considering severe smoothness assumption on the solutions: the solvent and the dissolve drug were <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span>- functions. In the present work, our aim is to establish second order estimates for the same variables reducing the smoothness assumption, namely, we assume that the solvent and the dissolved drug are <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>- functions. Numerical experiments illustrating the obtained theoretical results are also included.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"213 ","pages":"Pages 12-37"},"PeriodicalIF":2.2,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A tridiagonalization-based arbitrary-stride reduction approach for (p,q)-pentadiagonal linear systems

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-02-25 DOI: 10.1016/j.apnum.2025.02.017

Yi-Fan Wang, Ji-Teng Jia, Xin Fan

As a generalization of pentadiagonal matrices,

(p, q)

-pentadiagonal matrices have recently attracted considerable interest. In this paper, we first present an arbitrary-stride reduction for block diagonal linear systems composed of M-tridiagonal matrices. Building upon this reduction method and a reliable tridiagonalization process, we propose a tridiagonalization-based arbitrary-stride reduction approach for the

(p, q)

-pentadiagonal linear systems. Also, we elucidate eigenvalue clustering of coefficient matrices in the step-by-step process of the stride reduction. Numerical experiments are provided to illustrate the effectiveness of our proposed approach, implementing all experiments using MATLAB programs on a computer.

引用次数: 0

A novel projection-based method for monotone equations with Aitken Δ2 acceleration and its application to sparse signal restoration

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-02-21 DOI: 10.1016/j.apnum.2025.02.013

Ahmad Kamandi

In this paper, a novel projection method for solving systems of monotone equations is introduced. The method, employs a search direction based on the normalized negative residual and incorporates a suitable linesearch technique to determine the step length. An accelerated variant is also developed using a vector generalization of the Aitken

Δ^{2}

method, enhanced with a convergence safeguard. These methods are both derivative-free and computationally inexpensive, making them suitable for large-scale problems. The global convergence of these methods is established under specific conditions, and their superior efficiency is demonstrated through numerical tests on large-scale test problems, outperforming several recent accelerated algorithms. Finally, the application of these methods to the signal restoration problem is also discussed.

引用次数: 0

Convergence analysis of weak Galerkin finite element variable-time-step BDF2 implicit scheme for parabolic equations

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-02-21 DOI: 10.1016/j.apnum.2025.02.015

Chenxing Li , Fuzheng Gao , Jintao Cui

In this paper, we propose a fully discrete implicit method for parabolic problem. The variable-time-step BDF2 method is applied in time combining with the weak Galerkin finite element method in space. Optimal error estimates of

O (h^{r} + τ^{2})

H^{1}

-norm and

O (h^{r + 1} + τ^{2})

L^{2}

-norm are derived under the time-step ratio

0 < r_{k} ⩽ 4.8645

. Numerical experiments confirm the theoretical findings. Furthermore, an adaptive scheme is introduced and validated to enhance the computational performance.

引用次数: 0

A decoupled nonconforming finite element method for biharmonic equation in three dimensions

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-02-19 DOI: 10.1016/j.apnum.2025.02.012

Xuewei Cui, Xuehai Huang

This study focuses on a low-order decoupled nonconforming finite element method for solving the three-dimensional biharmonic equation. The main contribution is to discretize the generalized Stokes equation using a low-order nonconforming element for the

H_{0}^{1} (Ω; R^{3})

space and the lowest order edge element for the pressure. Additionally, the method employs the Lagrange element to solve the Poisson equations. To validate the theoretical convergence rates, numerical experiments are conducted.

引用次数: 0

A mixed discontinuous Galerkin method for the Biot equations

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-02-19 DOI: 10.1016/j.apnum.2025.02.011

Jing Wen

The Biot model is a coupling problem between the elastic media material with small deformation and porous media fluid flow, its mixed formulation uses the pore pressure, fluid flux, displacement as well as total stress tensor as the primary unknown variables. In this article, combining the discontinuous Galerkin method and the backward Euler method, we propose a mixed discontinuous Galerkin (MDG) method for the mixed Biot equations, it is based on coupling two MDG methods for each subproblem: the MDG method for the porous media fluid flow subproblem and the Hellinger-Reissner formulation of linear elastic subproblem. Then, we prove the well-posedness and the optimal priori error estimates for the MDG method under suitable norms. In particular, the optimal convergence rate of the pressure, displacement and stress tensor in discrete

L^{\infty} (L^{2})

norm and the fluid flux in discrete

L^{2} (L^{2})

norm are proved when the storage coefficient

c_{0}

is strictly positive. Similarly, we deduce the optimal convergence rate of all variables in discrete

L^{2} (L^{2})

norm when

c_{0}

is nonnegative. Finally, some numerical experiments are given to examine the convergence analysis.

{"title":"A mixed discontinuous Galerkin method for the Biot equations","authors":"Jing Wen","doi":"10.1016/j.apnum.2025.02.011","DOIUrl":"10.1016/j.apnum.2025.02.011","url":null,"abstract":"<div><div>The Biot model is a coupling problem between the elastic media material with small deformation and porous media fluid flow, its mixed formulation uses the pore pressure, fluid flux, displacement as well as total stress tensor as the primary unknown variables. In this article, combining the discontinuous Galerkin method and the backward Euler method, we propose a mixed discontinuous Galerkin (MDG) method for the mixed Biot equations, it is based on coupling two MDG methods for each subproblem: the MDG method for the porous media fluid flow subproblem and the Hellinger-Reissner formulation of linear elastic subproblem. Then, we prove the well-posedness and the optimal priori error estimates for the MDG method under suitable norms. In particular, the optimal convergence rate of the pressure, displacement and stress tensor in discrete <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> norm and the fluid flux in discrete <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> norm are proved when the storage coefficient <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is strictly positive. Similarly, we deduce the optimal convergence rate of all variables in discrete <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> norm when <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is nonnegative. Finally, some numerical experiments are given to examine the convergence analysis.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 283-299"},"PeriodicalIF":2.2,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An efficient two-grid algorithm based on Newton iteration for the stationary inductionless magnetohydrodynamic system

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-02-19 DOI: 10.1016/j.apnum.2025.02.009

Yande Xia , Yun-Bo Yang

In this paper, we propose and analyze a two-grid algorithm based on Newton iteration for solving the stationary inductionless magnetohydrodynamic system. The method involves first solving a small nonlinear system on a coarse grid with grid size H, followed by solving two linear problems on a fine grid with grid size h. These linear problems share the same stiffness matrix but differ only in their right-hand sides. The scaling between the coarse and fine grids is improved by our new method, while the approximate solution retains the same order of convergence as that observed in conventional methods. Furthermore,

H_{0} (div, Ω) \times L_{0}^{2} (Ω)

-conforming finite element pairs are utilized to discretize the current density and electric potential, ensuring that the discrete current density is exactly divergence-free. Stability and convergence analyses are rigorously derived, and

L^{2}

-error estimates for the velocity are provided. Numerical experiments are presented to verify the theoretical predictions and demonstrate the efficiency of the proposed method.

{"title":"An efficient two-grid algorithm based on Newton iteration for the stationary inductionless magnetohydrodynamic system","authors":"Yande Xia , Yun-Bo Yang","doi":"10.1016/j.apnum.2025.02.009","DOIUrl":"10.1016/j.apnum.2025.02.009","url":null,"abstract":"<div><div>In this paper, we propose and analyze a two-grid algorithm based on Newton iteration for solving the stationary inductionless magnetohydrodynamic system. The method involves first solving a small nonlinear system on a coarse grid with grid size <em>H</em>, followed by solving two linear problems on a fine grid with grid size <em>h</em>. These linear problems share the same stiffness matrix but differ only in their right-hand sides. The scaling between the coarse and fine grids is improved by our new method, while the approximate solution retains the same order of convergence as that observed in conventional methods. Furthermore, <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mrow><mi>div</mi></mrow><mo>,</mo><mi>Ω</mi><mo>)</mo><mo>×</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span>-conforming finite element pairs are utilized to discretize the current density and electric potential, ensuring that the discrete current density is exactly divergence-free. Stability and convergence analyses are rigorously derived, and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-error estimates for the velocity are provided. Numerical experiments are presented to verify the theoretical predictions and demonstrate the efficiency of the proposed method.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 312-332"},"PeriodicalIF":2.2,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Applied Numerical Mathematics

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀