Common problems in engineering projects that involve artificial ground freezing of soil or rock include inadequate thickness,strength and continuity of artificial frozen walls.It is difficult to evaluate the freezing ...Common problems in engineering projects that involve artificial ground freezing of soil or rock include inadequate thickness,strength and continuity of artificial frozen walls.It is difficult to evaluate the freezing state using only a few thermometer holes at fixed positions or with other existing approaches.Here we report a novel experimental design that investigates changes in ultrasonic properties(received waveform,wave velocity V_(p),wave amplitude,frequency spectrum,centroid frequency f_(c),kurtosis of the frequency spectrum KFS,and quality factor Q)measured during upward freezing,compared with those during uniform freezing,in order to determine the freezing state in 150 mm cubic blocks of Ardingly sandstone.Water content,porosity and density were estimated during upward freezing to ascertain water migration and changes of porosity and density at different stages.The period of receiving the wave increased substantially and coda waves changed from loose to compact during both upward and uniform freezing.The trend of increasing V_(p) can be divided into three stages during uniform freezing.During upward freezing,V_(p) increased more or less uniformly.The frequency spectrum could be used as a convenient and rapid method to identify different freezing states of sandstone(unfrozen,upward frozen,and uniformly frozen).The continuous changes in reflection coefficient r_(φ),refraction coefficient t_(φ) and acoustic impedance field are the major reason for larger reflection and refraction during upward freezing compared with uniform freezing.Wave velocity V_(p),wave amplitude A_(h),centroid frequency f_(c) and quality factor Q were adopted as ultrasonic parameters to evaluate quantitatively the temperature T of uniformly frozen sandstone,and their application within a radar chart is recommended.Determination of V_(p) provides a convenient method to evaluate the freezing state and calculate the cryofront height and frozen section thickness of upward frozen sandstone,with accuracies of 73.37%-99.23%.展开更多
In Multi-access Edge Computing(MEC),to deal with multiple user equipment(UE)’s task offloading problem of parallel relationships under the multi-constraints,this paper proposes a cooperation partial task offloading m...In Multi-access Edge Computing(MEC),to deal with multiple user equipment(UE)’s task offloading problem of parallel relationships under the multi-constraints,this paper proposes a cooperation partial task offloading method(named CPMM),aiming to reduce UE’s energy and computation consumption,while meeting the task completion delay as much as possible.CPMM first studies the task offloading of single-UE and then considers the task offloading ofmulti-UE based on single-UE task offloading.CPMMuses the critical path algorithmto divide the modules into key and non-key modules.According to some constraints of UE-self when offloading tasks,it gives priority to non-key modules for offloading and uses the evaluation decision method to select some appropriate key modules for offloading.Based on fully considering the competition between multiple UEs for communication resources and MEC service resources,CPMM uses the weighted queuing method to alleviate the competition for communication resources and uses the branch decision algorithm to determine the location of module offloading by BS according to the MEC servers’resources.It achieves its goal by selecting reasonable modules to offload and using the cooperation ofUE,MEC,andCloudCenter to determine the execution location of themodules.Extensive experiments demonstrate that CPMM obtains superior performances in task computation consumption reducing around 6%on average,task completion delay reducing around 5%on average,and better task execution success rate than other similar methods.展开更多
Micro RNAs(mi RNAs)act as regulators of plant development and multiple stress responses.Here we demonstrate that the rice mi R171 b-SCL6-IIs module regulates the balance between blast resistance,grain yield,and flower...Micro RNAs(mi RNAs)act as regulators of plant development and multiple stress responses.Here we demonstrate that the rice mi R171 b-SCL6-IIs module regulates the balance between blast resistance,grain yield,and flowering.mi R171 b-overexpressing rice plants(OX171 b)displayed increased rice blast resistance accompanied with enhanced defense responses and late heading,whereas blocking mi R171 b expression in rice(MIM171)led to greater susceptibility to blast disease,associated with compromised defense responses and early heading.Either overexpressing or silencing of mi R171 b significantly affected plant height and number of filled seeds per panicle(seed-setting rate),resulting in decreased grain yield.mi R171 b targets SCL6-IIa,SCL6-IIb,and SCL6-IIc,whose expression was suppressed in OX171 b but increased in MIM171.Mutants of SCL6-IIa,SCL6-IIb,and SCL6-IIc all displayed phenotypes like that of OX171 b,including markedly increased blast disease resistance,slightly decreased grain yield,and delayed flowering.Amounts of mi R171 b increased gradually in leaves during the vegetative stage but decreased gradually in panicles during the reproductive stage,whereas SCL6-IIs displayed the reverse expression pattern.Together,these results suggest that the expression of mi R171 b was time-and space-dependent during the rice growth period and regulated the balance between rice blast disease resistance,grain yield,and flowering via SCL6-IIs,and that appropriate accumulation of mi R171 b is essential for rice development.展开更多
The numerical computation of nonlocal Schrödinger equations (SEs) on the whole real axis is considered. Based on the artifcial boundary method, we frst derive the exact artifcial nonrefecting boundary conditions....The numerical computation of nonlocal Schrödinger equations (SEs) on the whole real axis is considered. Based on the artifcial boundary method, we frst derive the exact artifcial nonrefecting boundary conditions. For the numerical implementation, we employ the quadrature scheme proposed in Tian and Du (SIAM J Numer Anal 51:3458-3482, 2013) to discretize the nonlocal operator, and apply the z-transform to the discrete nonlocal system in an exterior domain, and derive an exact solution expression for the discrete system. This solution expression is referred to our exact nonrefecting boundary condition and leads us to reformulate the original infnite discrete system into an equivalent fnite discrete system. Meanwhile, the trapezoidal quadrature rule is introduced to discretize the contour integral involved in exact boundary conditions. Numerical examples are fnally provided to demonstrate the efectiveness of our approach.展开更多
[Objectives]To explore the mechanism of Angelica sinensis-Phellodendri Chinensis Cortex in the treatment of chronic prostatitis(CP)based on the method of network pharmacology.[Methods]The active components and action ...[Objectives]To explore the mechanism of Angelica sinensis-Phellodendri Chinensis Cortex in the treatment of chronic prostatitis(CP)based on the method of network pharmacology.[Methods]The active components and action targets of Angelica sinensis-Phellodendri Chinensis Cortex were screened by(TCMSP),a systematic pharmacological analysis platform of traditional Chinese medicine,combined with literature search.The target was corrected by Uniprot database,and the disease CP target was screened by GeneCards and OMIM database.The common targets of drugs and diseases were screened by R language software,and the visual network map of drugs-active components-targets-diseases was constructed by Cytoscape 3.5.1 software.The common target protein-protein interaction(PPI)network was constructed by using STRING platform.The R language software was used to annotate and analyze the gene function and pathway of the core target through geneontology(GO)and Kyoto Encyclopedia of Genes and Genomes(KEGG).[Results]46 active components of Angelica sinensis-Phellodendri Chinensis Cortex were screened,and 212 related targets were predicted,of which 159 were related to disease.These targets were mainly involved in biological processes such as heterologous biological stimulation,oxidation and anti-oxidation,and were mainly concentrated in PI3K-Akt,mitogen-activated protein kinase(MAPK),hypoxia inducible factor-1(HIF-1)and other related signaling pathways.[Conclusions]The multi-component,multi-target and multi-pathway action characteristics of Angelica sinensis-Phellodendri Chinensis Cortex were confirmed by network pharmacology,and the possible mechanism of Angelica sinensis-Phellodendri Chinensis Cortex in the treatment of CP was predicted,which provided a theoretical basis for further experiments to verify its action mechanism.展开更多
Boundary integral equations provide a powerful tool for the solution of scattering problems.However,often a singular kernel arises,in which case the standard quadratures will give rise to unavoidable deteriorations in...Boundary integral equations provide a powerful tool for the solution of scattering problems.However,often a singular kernel arises,in which case the standard quadratures will give rise to unavoidable deteriorations in numerical precision,thus special treatment is needed to handle the singular behavior.Especially,for inhomogeneous media,it is difficult if not impossible to find out an analytical expression for Green’s function.In this paper,an efficient fourth-order accurate Cartesian grid-based method is proposed for the two-dimensional Helmholtz scattering and transmission problems with inhomogeneous media.This method provides an alternative approach to indirect integral evaluation by solving equivalent interface problems on Cartesian grid with a modified fourth-order accurate compact finite difference scheme and a fast Fourier transform preconditioned conjugate gradient(FFT-PCG)solver.A remarkable point of this method is that there is no need to know analytical expressions for Green’s function.Numerical experiments are provided to demonstrate the advantage of the current approach,including its simplicity in implementation,its high accuracy and efficiency.展开更多
An essential feature of the subdiffusion equations with theα-order time fractional derivative is the weak singularity at the initial time.The weak regularity of the solution is usually characterized by a regularity p...An essential feature of the subdiffusion equations with theα-order time fractional derivative is the weak singularity at the initial time.The weak regularity of the solution is usually characterized by a regularity parameterσ∈(0,1)∪(1,2).Under this general regularity assumption,we present a rigorous analysis for the truncation errors and develop a new tool to obtain the stability results,i.e.,a refined discrete fractional-type Grönwall inequality(DFGI).After that,we obtain the pointwise-in-time error estimate of the widely used L1 scheme for nonlinear subdiffusion equations.The present results fill the gap on some interesting convergence results of L1 scheme onσ∈(0,α)∪(α,1)∪(1,2].Numerical experiments are provided to demonstrate the effectiveness of our theoretical analysis.展开更多
CORRECTION TO:PROTEIN CELL(2014)5(11):851-861 HTTPS://DOI.ORG/10.1007/S13238-014-0093-5 In the original publication the display of Fig.1 is in correct.The correct Fig.1 is available in this correction.
Digital holography possesses the advantages of wide-field,non-contact,precise,and dynamic measurements for the complex amplitude of object waves.Today,digital holography and its derivatives have been widely applied in...Digital holography possesses the advantages of wide-field,non-contact,precise,and dynamic measurements for the complex amplitude of object waves.Today,digital holography and its derivatives have been widely applied in interferometric measurements,three-dimensional imaging,and quantitative phase imaging,demonstrating significant potential in the material science,industry,and biomedical fields,among others.However,in conventional off-axis holographic experimental setups,the object and reference beams propagate in separated paths,resulting in low temporal stability and measurement sensitivity.By designing common-path configurations where the two interference beams share the same or similar paths,environmental disturbance to the two beams can be effectively compensated.Therefore,the temporal stability of the experimental setups for hologram recording can be significantly improved for time-lapsing measurements.In this review,we categorise the common-path models as lateral shearing,point diffraction,and other types based on the different approaches to generate the reference beam.Benefiting from compact features,common-path digital holography is extremely promising for the manufacture of highly stable optical measurement and imaging instruments in the future.展开更多
This paper is concerned with numerical computations of a class of biologi-cal models on unbounded spatial domains.To overcome the unboundedness of spatial domain,we first construct efficient local absorbing boundary c...This paper is concerned with numerical computations of a class of biologi-cal models on unbounded spatial domains.To overcome the unboundedness of spatial domain,we first construct efficient local absorbing boundary conditions(LABCs)to re-formulate the Cauchy problem into an initial-boundary value(IBV)problem.After that,we construct a linearized finite difference scheme for the reduced IVB problem,and provide the corresponding error estimates and stability analysis.The delay-dependent dynamical properties on the Nicholson’s blowflies equation and the Mackey-Glass equa-tion are numerically investigated.Finally,numerical examples are given to demonstrate the efficiency of our LABCs and theoretical results of the numerical scheme.展开更多
We consider the computation of a nonlocal Helmholtz equation by using perfectly matched layer(PML).We first derive the nonlocal PML equation by extending PML modifications from the local operator to the nonlocal opera...We consider the computation of a nonlocal Helmholtz equation by using perfectly matched layer(PML).We first derive the nonlocal PML equation by extending PML modifications from the local operator to the nonlocal operator of integral form.After that,we give stability estimates of some weighted-average values of the nonlocal Helmholtz solution and prove that(i)the weighted-average value of the nonlocal PML solution decays exponentially in PML layers in one case;(ii)in the other case,the weighted-average value of the nonlocal Helmholtz solution itself decays exponentially outside some domain.Particularly for a typical kernel functionγ_(1)(s)=1/2 e^(−|s|),we obtain the Green’s function of the nonlocal Helmholtz equation,and use the Green’s function to further prove that(i)the nonlocal PML solution decays exponentially in PML layers in one case;(ii)in the other case,the nonlocal Helmholtz solution itself decays exponentially outside some domain.Based on our theoretical analysis,the truncated nonlocal problems are discussed and an asymptotic compatibility scheme is also introduced to solve the resulting truncated problems.Finally,numerical examples are provided to verify the effectiveness and validation of our nonlocal PML strategy and theoretical findings.展开更多
The aim of this paper is to derive a stable and efficient scheme for solving the one-dimensional time-fractional nonlinear Schrodinger equation set in an unbounded domain.We first derive absorbing boundary conditions ...The aim of this paper is to derive a stable and efficient scheme for solving the one-dimensional time-fractional nonlinear Schrodinger equation set in an unbounded domain.We first derive absorbing boundary conditions for the fractional system by using the unified approach introduced in[47,48]and a linearization procedure.Then,the initial boundary-value problem for the fractional system with ABCs is discretized,a stability analysis is developed and the error estimate O(h^(2)+τ)is stated.To accel-erate the L1-scheme in time,a sum-of-exponentials approximation is introduced to speed-up the evaluation of the Caputo fractional derivative.The resulting algorithm is highly efficient for long time simulations.Finally,we end the paper by reporting some numerical simulations to validate the properties(accuracy and efficiency)of the derived scheme.展开更多
This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-Galerkin finite element methods.The analysis of L1 methods for time-fractional nonlinear problems is li...This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-Galerkin finite element methods.The analysis of L1 methods for time-fractional nonlinear problems is limited mainly due to the lack of a fundamental Gronwall type inequality.In this paper,we establish such a fundamental inequality for the L1 approximation to the Caputo fractional derivative.In terms of the Gronwall type inequality,we provide optimal error estimates of several fully discrete linearized Galerkin finite element methods for nonlinear problems.The theoretical results are illustrated by applying our proposed methods to the time fractional nonlinear Huxley equation and time fractional Fisher equation.展开更多
This paper is concerned with numerical approximations of a nonlocal heat equation define on an infinite domain.Two classes of artificial boundary conditions(ABCs)are designed,namely,nonlocal analog Dirichlet-to-Neuman...This paper is concerned with numerical approximations of a nonlocal heat equation define on an infinite domain.Two classes of artificial boundary conditions(ABCs)are designed,namely,nonlocal analog Dirichlet-to-Neumann-type ABCs(global in time)and high-order Pad´e approximate ABCs(local in time).These ABCs reformulate the original problem into an initial-boundary-value(IBV)problem on a bounded domain.For the global ABCs,we adopt a fast evolution to enhance computational efficiency and reduce memory storage.High order fully discrete schemes,both second-order in time and space,are given to discretize two reduced problems.Extensive numerical experiments are carried out to show the accuracy and efficiency of the proposed methods.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.51804157,51774183,and 11702094)the University of Sussex,UK.Both are gratefully acknowledged.
文摘Common problems in engineering projects that involve artificial ground freezing of soil or rock include inadequate thickness,strength and continuity of artificial frozen walls.It is difficult to evaluate the freezing state using only a few thermometer holes at fixed positions or with other existing approaches.Here we report a novel experimental design that investigates changes in ultrasonic properties(received waveform,wave velocity V_(p),wave amplitude,frequency spectrum,centroid frequency f_(c),kurtosis of the frequency spectrum KFS,and quality factor Q)measured during upward freezing,compared with those during uniform freezing,in order to determine the freezing state in 150 mm cubic blocks of Ardingly sandstone.Water content,porosity and density were estimated during upward freezing to ascertain water migration and changes of porosity and density at different stages.The period of receiving the wave increased substantially and coda waves changed from loose to compact during both upward and uniform freezing.The trend of increasing V_(p) can be divided into three stages during uniform freezing.During upward freezing,V_(p) increased more or less uniformly.The frequency spectrum could be used as a convenient and rapid method to identify different freezing states of sandstone(unfrozen,upward frozen,and uniformly frozen).The continuous changes in reflection coefficient r_(φ),refraction coefficient t_(φ) and acoustic impedance field are the major reason for larger reflection and refraction during upward freezing compared with uniform freezing.Wave velocity V_(p),wave amplitude A_(h),centroid frequency f_(c) and quality factor Q were adopted as ultrasonic parameters to evaluate quantitatively the temperature T of uniformly frozen sandstone,and their application within a radar chart is recommended.Determination of V_(p) provides a convenient method to evaluate the freezing state and calculate the cryofront height and frozen section thickness of upward frozen sandstone,with accuracies of 73.37%-99.23%.
文摘In Multi-access Edge Computing(MEC),to deal with multiple user equipment(UE)’s task offloading problem of parallel relationships under the multi-constraints,this paper proposes a cooperation partial task offloading method(named CPMM),aiming to reduce UE’s energy and computation consumption,while meeting the task completion delay as much as possible.CPMM first studies the task offloading of single-UE and then considers the task offloading ofmulti-UE based on single-UE task offloading.CPMMuses the critical path algorithmto divide the modules into key and non-key modules.According to some constraints of UE-self when offloading tasks,it gives priority to non-key modules for offloading and uses the evaluation decision method to select some appropriate key modules for offloading.Based on fully considering the competition between multiple UEs for communication resources and MEC service resources,CPMM uses the weighted queuing method to alleviate the competition for communication resources and uses the branch decision algorithm to determine the location of module offloading by BS according to the MEC servers’resources.It achieves its goal by selecting reasonable modules to offload and using the cooperation ofUE,MEC,andCloudCenter to determine the execution location of themodules.Extensive experiments demonstrate that CPMM obtains superior performances in task computation consumption reducing around 6%on average,task completion delay reducing around 5%on average,and better task execution success rate than other similar methods.
基金supported by the National Natural Science Foundation of China(U19A2033,31672090,and 31430072)the Sichuan Applied Fundamental Research Foundation(2020YJ0332)to Wenming Wang。
文摘Micro RNAs(mi RNAs)act as regulators of plant development and multiple stress responses.Here we demonstrate that the rice mi R171 b-SCL6-IIs module regulates the balance between blast resistance,grain yield,and flowering.mi R171 b-overexpressing rice plants(OX171 b)displayed increased rice blast resistance accompanied with enhanced defense responses and late heading,whereas blocking mi R171 b expression in rice(MIM171)led to greater susceptibility to blast disease,associated with compromised defense responses and early heading.Either overexpressing or silencing of mi R171 b significantly affected plant height and number of filled seeds per panicle(seed-setting rate),resulting in decreased grain yield.mi R171 b targets SCL6-IIa,SCL6-IIb,and SCL6-IIc,whose expression was suppressed in OX171 b but increased in MIM171.Mutants of SCL6-IIa,SCL6-IIb,and SCL6-IIc all displayed phenotypes like that of OX171 b,including markedly increased blast disease resistance,slightly decreased grain yield,and delayed flowering.Amounts of mi R171 b increased gradually in leaves during the vegetative stage but decreased gradually in panicles during the reproductive stage,whereas SCL6-IIs displayed the reverse expression pattern.Together,these results suggest that the expression of mi R171 b was time-and space-dependent during the rice growth period and regulated the balance between rice blast disease resistance,grain yield,and flowering via SCL6-IIs,and that appropriate accumulation of mi R171 b is essential for rice development.
基金Jiwei Zhang is partially supported by the National Natural Science Foundation of China under Grant No.11771035the NSAF U1530401+3 种基金the Natural Science Foundation of Hubei Province No.2019CFA007Xiangtan University 2018ICIP01Chunxiong Zheng is partially supported by Natural Science Foundation of Xinjiang Autonom ous Region under No.2019D01C026the National Natural Science Foundation of China under Grant Nos.11771248 and 91630205。
文摘The numerical computation of nonlocal Schrödinger equations (SEs) on the whole real axis is considered. Based on the artifcial boundary method, we frst derive the exact artifcial nonrefecting boundary conditions. For the numerical implementation, we employ the quadrature scheme proposed in Tian and Du (SIAM J Numer Anal 51:3458-3482, 2013) to discretize the nonlocal operator, and apply the z-transform to the discrete nonlocal system in an exterior domain, and derive an exact solution expression for the discrete system. This solution expression is referred to our exact nonrefecting boundary condition and leads us to reformulate the original infnite discrete system into an equivalent fnite discrete system. Meanwhile, the trapezoidal quadrature rule is introduced to discretize the contour integral involved in exact boundary conditions. Numerical examples are fnally provided to demonstrate the efectiveness of our approach.
基金Nursery Project of Xiyuan Hospital of China Academy of Chinese Medical Sciences(2019XYMP-23)Clinical Study of Guihuang Prescription in the Treatment of Chronic Prostatitis/Chronic Pelvic Pain Syndrome Based on"Internal Elimination Method for Ulcer"+1 种基金National Natural Science Foundation Cultivation Project of Xiyuan Hospital of China Academy of Chinese Medical Sciences(XY20-13)Study on the Mechanism of Guihuang Prescription in the Treatment of Prostatitis III Based on PI3K/Akt/NF-κB Signaling Pathway.
文摘[Objectives]To explore the mechanism of Angelica sinensis-Phellodendri Chinensis Cortex in the treatment of chronic prostatitis(CP)based on the method of network pharmacology.[Methods]The active components and action targets of Angelica sinensis-Phellodendri Chinensis Cortex were screened by(TCMSP),a systematic pharmacological analysis platform of traditional Chinese medicine,combined with literature search.The target was corrected by Uniprot database,and the disease CP target was screened by GeneCards and OMIM database.The common targets of drugs and diseases were screened by R language software,and the visual network map of drugs-active components-targets-diseases was constructed by Cytoscape 3.5.1 software.The common target protein-protein interaction(PPI)network was constructed by using STRING platform.The R language software was used to annotate and analyze the gene function and pathway of the core target through geneontology(GO)and Kyoto Encyclopedia of Genes and Genomes(KEGG).[Results]46 active components of Angelica sinensis-Phellodendri Chinensis Cortex were screened,and 212 related targets were predicted,of which 159 were related to disease.These targets were mainly involved in biological processes such as heterologous biological stimulation,oxidation and anti-oxidation,and were mainly concentrated in PI3K-Akt,mitogen-activated protein kinase(MAPK),hypoxia inducible factor-1(HIF-1)and other related signaling pathways.[Conclusions]The multi-component,multi-target and multi-pathway action characteristics of Angelica sinensis-Phellodendri Chinensis Cortex were confirmed by network pharmacology,and the possible mechanism of Angelica sinensis-Phellodendri Chinensis Cortex in the treatment of CP was predicted,which provided a theoretical basis for further experiments to verify its action mechanism.
基金supported by the NSFC(Grant No.12001193),by the Scientific Research Fund of Hunan Provincial Education Department(Grant No.20B376)by the Key Projects of Hunan Provincial Department of Education(Grant No.22A033)+4 种基金by the Changsha Municipal Natural Science Foundation(Grant Nos.kq2014073,kq2208158).W.Ying is supported by the NSFC(Grant No.DMS-11771290)by the Science Challenge Project of China(Grant No.TZ2016002)by the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA25000400).J.Zhang was partially supported by the National Natural Science Foundation of China(Grant No.12171376)by the Fundamental Research Funds for the Central Universities(Grant No.2042021kf0050)by the Natural Science Foundation of Hubei Province(Grant No.2019CFA007).
文摘Boundary integral equations provide a powerful tool for the solution of scattering problems.However,often a singular kernel arises,in which case the standard quadratures will give rise to unavoidable deteriorations in numerical precision,thus special treatment is needed to handle the singular behavior.Especially,for inhomogeneous media,it is difficult if not impossible to find out an analytical expression for Green’s function.In this paper,an efficient fourth-order accurate Cartesian grid-based method is proposed for the two-dimensional Helmholtz scattering and transmission problems with inhomogeneous media.This method provides an alternative approach to indirect integral evaluation by solving equivalent interface problems on Cartesian grid with a modified fourth-order accurate compact finite difference scheme and a fast Fourier transform preconditioned conjugate gradient(FFT-PCG)solver.A remarkable point of this method is that there is no need to know analytical expressions for Green’s function.Numerical experiments are provided to demonstrate the advantage of the current approach,including its simplicity in implementation,its high accuracy and efficiency.
基金supported by the National Natural Science Foundation of China under grants 11771162,11771035,12171376 and 2020-JCJQ-ZD-029.
文摘An essential feature of the subdiffusion equations with theα-order time fractional derivative is the weak singularity at the initial time.The weak regularity of the solution is usually characterized by a regularity parameterσ∈(0,1)∪(1,2).Under this general regularity assumption,we present a rigorous analysis for the truncation errors and develop a new tool to obtain the stability results,i.e.,a refined discrete fractional-type Grönwall inequality(DFGI).After that,we obtain the pointwise-in-time error estimate of the widely used L1 scheme for nonlinear subdiffusion equations.The present results fill the gap on some interesting convergence results of L1 scheme onσ∈(0,α)∪(α,1)∪(1,2].Numerical experiments are provided to demonstrate the effectiveness of our theoretical analysis.
文摘CORRECTION TO:PROTEIN CELL(2014)5(11):851-861 HTTPS://DOI.ORG/10.1007/S13238-014-0093-5 In the original publication the display of Fig.1 is in correct.The correct Fig.1 is available in this correction.
基金Support from the National Natural Science Foundation of China(NSFC)(61927810,62075183,62005219)Fundamental Research Funds for the Central Universities(310202011qd004)is acknowledged.
文摘Digital holography possesses the advantages of wide-field,non-contact,precise,and dynamic measurements for the complex amplitude of object waves.Today,digital holography and its derivatives have been widely applied in interferometric measurements,three-dimensional imaging,and quantitative phase imaging,demonstrating significant potential in the material science,industry,and biomedical fields,among others.However,in conventional off-axis holographic experimental setups,the object and reference beams propagate in separated paths,resulting in low temporal stability and measurement sensitivity.By designing common-path configurations where the two interference beams share the same or similar paths,environmental disturbance to the two beams can be effectively compensated.Therefore,the temporal stability of the experimental setups for hologram recording can be significantly improved for time-lapsing measurements.In this review,we categorise the common-path models as lateral shearing,point diffraction,and other types based on the different approaches to generate the reference beam.Benefiting from compact features,common-path digital holography is extremely promising for the manufacture of highly stable optical measurement and imaging instruments in the future.
基金This work is supported in part by the National Natural Science Foun-dation of China(Grant Nos.11771162,11771035,11571027,91430216 and U1530401)Beijing Nova Program(No.Z151100003150140)Scientific Research Project of Beijing Educational Committee(No.KM201510005032).
文摘This paper is concerned with numerical computations of a class of biologi-cal models on unbounded spatial domains.To overcome the unboundedness of spatial domain,we first construct efficient local absorbing boundary conditions(LABCs)to re-formulate the Cauchy problem into an initial-boundary value(IBV)problem.After that,we construct a linearized finite difference scheme for the reduced IVB problem,and provide the corresponding error estimates and stability analysis.The delay-dependent dynamical properties on the Nicholson’s blowflies equation and the Mackey-Glass equa-tion are numerically investigated.Finally,numerical examples are given to demonstrate the efficiency of our LABCs and theoretical results of the numerical scheme.
基金supported by the NSFC(Grants No.11771035,12071401,12171376,2020-JCJQ-ZD-029)the Natural Science Foundation of Hunan Province(Grant No.2019JJ50572)+1 种基金the Natural Science Foundation of Hubei Province(Grant No.2019CFA007)the Xiangtan University(Grant No.2018ICIP01)。
文摘We consider the computation of a nonlocal Helmholtz equation by using perfectly matched layer(PML).We first derive the nonlocal PML equation by extending PML modifications from the local operator to the nonlocal operator of integral form.After that,we give stability estimates of some weighted-average values of the nonlocal Helmholtz solution and prove that(i)the weighted-average value of the nonlocal PML solution decays exponentially in PML layers in one case;(ii)in the other case,the weighted-average value of the nonlocal Helmholtz solution itself decays exponentially outside some domain.Particularly for a typical kernel functionγ_(1)(s)=1/2 e^(−|s|),we obtain the Green’s function of the nonlocal Helmholtz equation,and use the Green’s function to further prove that(i)the nonlocal PML solution decays exponentially in PML layers in one case;(ii)in the other case,the nonlocal Helmholtz solution itself decays exponentially outside some domain.Based on our theoretical analysis,the truncated nonlocal problems are discussed and an asymptotic compatibility scheme is also introduced to solve the resulting truncated problems.Finally,numerical examples are provided to verify the effectiveness and validation of our nonlocal PML strategy and theoretical findings.
基金supported by the NSFC under grants 11771035,91430216,U1530401supported by the NSFC under grants Nos.11571128,11771162support of the French ANR grant BOND(ANR-13-BS01-0009-01)and the LIASFMA(funding from the University of Lorraine).
文摘The aim of this paper is to derive a stable and efficient scheme for solving the one-dimensional time-fractional nonlinear Schrodinger equation set in an unbounded domain.We first derive absorbing boundary conditions for the fractional system by using the unified approach introduced in[47,48]and a linearization procedure.Then,the initial boundary-value problem for the fractional system with ABCs is discretized,a stability analysis is developed and the error estimate O(h^(2)+τ)is stated.To accel-erate the L1-scheme in time,a sum-of-exponentials approximation is introduced to speed-up the evaluation of the Caputo fractional derivative.The resulting algorithm is highly efficient for long time simulations.Finally,we end the paper by reporting some numerical simulations to validate the properties(accuracy and efficiency)of the derived scheme.
基金This work is supported by NSFC(Grant Nos.11771035,11771162,11571128,61473126,91430216,91530204,11372354 and U1530401),a grant from the RGC of HK 11300517,China(Project No.CityU 11302915),China Postdoctoral Science Foundation under grant No.2016M602273,a grant DRA2015518 from 333 High-level Personal Training Project of Jiangsu Province,and the USA National Science Foundation grant DMS-1315259the USA Air Force Office of Scientific Research grant FA9550-15-1-0001.Jiwei Zhang also thanks the hospitality of Hong Kong City University during the period of his visiting.
文摘This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-Galerkin finite element methods.The analysis of L1 methods for time-fractional nonlinear problems is limited mainly due to the lack of a fundamental Gronwall type inequality.In this paper,we establish such a fundamental inequality for the L1 approximation to the Caputo fractional derivative.In terms of the Gronwall type inequality,we provide optimal error estimates of several fully discrete linearized Galerkin finite element methods for nonlinear problems.The theoretical results are illustrated by applying our proposed methods to the time fractional nonlinear Huxley equation and time fractional Fisher equation.
基金This research is supported in part by the U.S.NSF grants DMS-1318586 and DMS-1315259AFOSR MURI Center for Material Failure Prediction Through Peridynamics,OSD/ARO/MURI W911NF-15-1-0562 on Fractional PDEs for Conservation Laws and Beyond:Theory,Numerics and Applicationsthe NSFC under grants 91430216 and the NSFC program for Scientific Research Center under program No.:U1530401.
文摘This paper is concerned with numerical approximations of a nonlocal heat equation define on an infinite domain.Two classes of artificial boundary conditions(ABCs)are designed,namely,nonlocal analog Dirichlet-to-Neumann-type ABCs(global in time)and high-order Pad´e approximate ABCs(local in time).These ABCs reformulate the original problem into an initial-boundary-value(IBV)problem on a bounded domain.For the global ABCs,we adopt a fast evolution to enhance computational efficiency and reduce memory storage.High order fully discrete schemes,both second-order in time and space,are given to discretize two reduced problems.Extensive numerical experiments are carried out to show the accuracy and efficiency of the proposed methods.