Quasi-solid electrolytes(QSEs)based on nanoporous materials are promising candidates to construct high-performance Limetal batteries(LMBs).However,simultaneously boosting the ionic conductivity(σ)and lithium-ion tran...Quasi-solid electrolytes(QSEs)based on nanoporous materials are promising candidates to construct high-performance Limetal batteries(LMBs).However,simultaneously boosting the ionic conductivity(σ)and lithium-ion transference number(t^(+)) of liquid electrolyte confined in porous matrix remains challenging.Herein,we report a novel Janus MOFLi/MSLi QSEs with asymmetric porous structure to inherit the benefits of both mesoporous and microporous hosts.This Janus QSE composed of mesoporous silica and microporous MOF exhibits a neat Li^(+) conductivity of 1.5.10^(–4)S cm^(−1) with t^(+) of 0.71.A partially de-solvated structure and preference distribution of Li^(+)near the Lewis base O atoms were depicted by MD simulations.Meanwhile,the nanoporous structure enabled efficient ion flux regulation,promoting the homogenous deposition of Li^(+).When incorporated in Li||Cu cells,the MOFLi/MSLi QSEs demonstrated a high Coulombic efficiency of 98.1%,surpassing that of liquid electrolytes(96.3%).Additionally,NCM 622||Li batteries equipped with MOFLi/MSLi QSEs exhibited promising rate performance and could operate stably for over 200 cycles at 1 C.These results highlight the potential of Janus MOFLi/MSLi QSEs as promising candidates for next-generation LMBs.展开更多
The first-principles calculations are performed to examine structural,mechanical,and electronic properties at large strain for a monolayer C_(4)N_(4),which has been predicted as an anchoring promising material to atte...The first-principles calculations are performed to examine structural,mechanical,and electronic properties at large strain for a monolayer C_(4)N_(4),which has been predicted as an anchoring promising material to attenuate shuttle effect in Li–S batteries stemming from its large absorption energy and low diffusion energy barrier.Our results show that the ideal strengths of C_(4)N_(4)under tension and pure shear deformation conditions reach 13.9 GPa and 12.5 GPa when the strains are 0.07 and 0.28,respectively.The folded five-membered rings and diverse bonding modes between carbon and nitrogen atoms enhance the ability to resist plastic deformation of C_(4)N_(4).The orderly bond-rearranging behaviors under the weak tensile loading path along the[100]direction cause the impressive semiconductor–metal transition and inverse semiconductor–metal transition.The present results enrich the knowledge of the structure and electronic properties of C_(4)N_(4)under deformations and shed light on exploring other two-dimensional materials under diverse loading conditions.展开更多
Background:Excessive exudate secreted from chronic wounds often leads to overhydration and infection.Although a variety of dressings are currently available in clinical applications,they frequently fail to provide mul...Background:Excessive exudate secreted from chronic wounds often leads to overhydration and infection.Although a variety of dressings are currently available in clinical applications,they frequently fail to provide multifunction to promote chronic wound healing.The dressings with a Janus structure,featuring distinct properties on each side,are potential to improve wound healing.Methods:Composite dressings with a Janus structure were fabricated,comprising freeze-dried polycaprolactone(PCL)electrospun membrane and alginate-based hydrogel.The PCL fibrous membrane provided air permeability,while the hydrogel loaded with Deferoxamine,composed of alginate and poly(N-isopropylacrylamide)(PNIPAM),exhibited hygroscopic properties.The inclusion of PNIPAM imparted thermo-responsivity.Results:The hydrogel(thickness of 2.778±0.082 mm)exhibited a robust adhesion to the fiber membrane(thickness of 0.261±0.041 mm).For ANDC(Alginate-PNIPAM hydrogel with Deferoxamine/PCL membrane)samples,the water vapor transmission rate(WVTR)was measured to be 3364.80±23.23 g∙m−2∙day−1 and the swelling ratio at 2 h was determined to be 1179±125%.The thermo-responsivity of ANDC samples manifested in an increased swelling rate,escalating from 797±189%at 37°C to 1132±147%at 4°C.The elastic modulus was assessed for lyophilized and rehydrated ANDC sample.When theωof the rheometer rotor was decreased from 10 rad/s to 0.1 rad/s,the lyophilized dressing exhibited a decrease from 2.65±0.01 MPa to 1.80±0.90 MPa,while the rehydrated dressing demonstrated an increase from 133.65±55.68 Pa to 264.23±141.71 Pa.The pro-healing properties of the dressings were evaluated using full-thickness skin defect model on SD rats,and a circular wound of diameter 10 mm healed completely by day 12.Conclusion:The dressings not only protected the wound and absorbed excess exudate,but also demonstrated nondestructive peelability upon cooling,providing a novel approach for accelerating wound healing and management.展开更多
Direct-write atom lithography,one of the potential nanofabrication techniques,is restricted by some difficulties in producing optical masks for the deposition of complex structures.In order to make further progress,a ...Direct-write atom lithography,one of the potential nanofabrication techniques,is restricted by some difficulties in producing optical masks for the deposition of complex structures.In order to make further progress,a structured mirror array is developed to transversely collimate the chromium atomic beam in two dimensions.The best collimation is obtained when the laser red detunes by natural line-width of transition 7S3 → 7P40 of the chromium atom.The collimation ratio is 0.45 vertically（in x axis）,and it is 0.55 horizontally（in y axis）.The theoretical model is also simulated,and success of our structured mirror array is achieved.展开更多
Several natural organism can change shape under external stimuli. These natural phenomena have inspired a vast amount of research on exploration and implementation of reconfigurable shape transformation. The Janus str...Several natural organism can change shape under external stimuli. These natural phenomena have inspired a vast amount of research on exploration and implementation of reconfigurable shape transformation. The Janus structure is a promising approach to achieve shape transformation based on its heterogeneous chemical or physical properties on opposite sides.However, the heterogeneity is generally realized by multi-step processing, different materials,and/or different processing parameters. Here, we present a simple and flexible method of producing p H-sensitive Janus microactuators from a single material, using the same laser printing parameters. These microactuators exhibit reversible structural deformations with large bending angles of ~31°and fast response(~0.2 s) by changing the p H value of the aqueous environment. Benefited from the high flexibility of the laser printing technique and the spatial arrangements, pillar heights, and bending directions of microactuators are readily controlled,enabling a variety of switchable ordered patterns and complex petal-like structures on flat surfaces and inside microchannels. Finally, we explore the potential applications of this method in information encryption/decryption and microtarget capturing.展开更多
Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic c...Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic crystals for TE and TM waves are different from the two-dimensional conventional photonic crystals. Some absolute band gaps and semiDirac points are found. When the medium column radius and the function form of the dielectric constant are modulated, the numbers, width, and position of band gaps are changed, and the semi-Dirac point can either occur or disappear. Therefore,the special band gaps structures and semi-Dirac points can be achieved through the modulation on the two-dimensional function photonic crystals. The results will provide a new design method of optical devices based on the two-dimensional function photonic crystals.展开更多
The algebraic solitary wave and its associated eigenvalue problem in a deep stratified fluid with a free surface and a shallow upper layer were studied. And its vertical structure was examined. An exact solution for t...The algebraic solitary wave and its associated eigenvalue problem in a deep stratified fluid with a free surface and a shallow upper layer were studied. And its vertical structure was examined. An exact solution for the derived 2D Benjamin-Ono equation was obtained, and physical explanation was given with the corresponding dispersion relation. As a special case, the vertical structure of the weakly nonlinear internal wave for the Holmboe density distribution was numerically investigated, and the propagating mechanism of the internal wave was studied by using the ray theory.展开更多
Two-dimensional(2D)magnetic materials have attracted tremendous research interest because of the promising application in the next-generation microelectronic devices.Here,by the first-principles calculations,we propos...Two-dimensional(2D)magnetic materials have attracted tremendous research interest because of the promising application in the next-generation microelectronic devices.Here,by the first-principles calculations,we propose a twodimensional ferromagnetic material with high Curie temperature,manganese tetranitride MnN4monolayer,which is a square-planar lattice made up of only one layer of atoms.The structure is demonstrated to be stable by the phonon spectra and the molecular dynamic simulations,and the stability is ascribed to theπ–d conjugation betweenπorbital of N=N bond and d orbital of Mn.More interestingly,the MnN_(4)monolayer displays robust 2D ferromagnetism,which originates from the strong exchange couplings between Mn atoms due to theπ–d conjugation.The high critical temperature of 247 K is determined by solving the Heisenberg model using the Monte Carlo method.展开更多
Characterizing the trajectory of the healthy aging brain and exploring age-related structural changes in the brain can help deepen our understanding of the mechanism of brain aging.Currently,most structural magnetic r...Characterizing the trajectory of the healthy aging brain and exploring age-related structural changes in the brain can help deepen our understanding of the mechanism of brain aging.Currently,most structural magnetic resonance imaging literature explores brain aging merely from the perspective of morphological features,which cannot fully utilize the grayscale values containing important intrinsic information about brain structure.In this study,we propose the construction of two-dimensional horizontal visibility graphs based on the pixel intensity values of the gray matter slices directly.Normalized network structure entropy(NNSE)is then introduced to quantify the overall heterogeneities of these graphs.The results demonstrate a decrease in the NNSEs of gray matter with age.Compared with the middle-aged and the elderly,the larger values of the NNSE in the younger group may indicate more homogeneous network structures,smaller differences in importance between nodes and thus a more powerful ability to tolerate intrusion.In addition,the hub nodes of different adult age groups are primarily located in the precuneus,cingulate gyrus,superior temporal gyrus,inferior temporal gyrus,parahippocampal gyrus,insula,precentral gyrus and postcentral gyrus.Our study can provide a new perspective for understanding and exploring the structural mechanism of brain aging.展开更多
Electrocatalytic CO_(2) reduction reaction(eCO_(2) RR)has significant relevance to settle the global energy crisis and abnormal climate problem via mitigating the excess emission of waste CO_(2) and producing high-val...Electrocatalytic CO_(2) reduction reaction(eCO_(2) RR)has significant relevance to settle the global energy crisis and abnormal climate problem via mitigating the excess emission of waste CO_(2) and producing high-value-added chemicals.Currently,eCO_(2) RR to formic acid or formate is one of the most technologically and economically viable approaches to realize high-efficiency CO_(2) utilization,and the development of efficient electrocatalysts is very urgent to achieve efficient and stable catalytic performance.In this review,the recent advances for two-dimensional bismuth-based nanosheets(2D Bi-based NSs)electrocatalysts are concluded from both theoretical and experimental perspectives.Firstly,the preparation strategies of 2D Bi-based NSs in aspects to precisely control the thickness and uniformity are summarized.In addition,the electronic regulation strategies of 2D Bi-based NSs are highlighted to gain insight into the effects of the structure-property relationship on facilitating CO_(2) activation,improving product selectivity,and optimizing carrier transport dynamics.Finally,the considerable challenges and opportunities of 2D Bi-based NSs are discussed to lighten new directions for future research of eCO_(2) RR.展开更多
We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent devel...We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.展开更多
基金supported by National Natural Science Foundation of China(Grant No.22005266)Zhejiang Provincial Natural Science Foundation(Grant No.LR21E020003)“the Fundamental Research Funds for the Central Universities”(2021FZZX001-09).
文摘Quasi-solid electrolytes(QSEs)based on nanoporous materials are promising candidates to construct high-performance Limetal batteries(LMBs).However,simultaneously boosting the ionic conductivity(σ)and lithium-ion transference number(t^(+)) of liquid electrolyte confined in porous matrix remains challenging.Herein,we report a novel Janus MOFLi/MSLi QSEs with asymmetric porous structure to inherit the benefits of both mesoporous and microporous hosts.This Janus QSE composed of mesoporous silica and microporous MOF exhibits a neat Li^(+) conductivity of 1.5.10^(–4)S cm^(−1) with t^(+) of 0.71.A partially de-solvated structure and preference distribution of Li^(+)near the Lewis base O atoms were depicted by MD simulations.Meanwhile,the nanoporous structure enabled efficient ion flux regulation,promoting the homogenous deposition of Li^(+).When incorporated in Li||Cu cells,the MOFLi/MSLi QSEs demonstrated a high Coulombic efficiency of 98.1%,surpassing that of liquid electrolytes(96.3%).Additionally,NCM 622||Li batteries equipped with MOFLi/MSLi QSEs exhibited promising rate performance and could operate stably for over 200 cycles at 1 C.These results highlight the potential of Janus MOFLi/MSLi QSEs as promising candidates for next-generation LMBs.
基金Project support by the National Natural Science Foundation of China(Grant Nos.11704044 and 12074140)。
文摘The first-principles calculations are performed to examine structural,mechanical,and electronic properties at large strain for a monolayer C_(4)N_(4),which has been predicted as an anchoring promising material to attenuate shuttle effect in Li–S batteries stemming from its large absorption energy and low diffusion energy barrier.Our results show that the ideal strengths of C_(4)N_(4)under tension and pure shear deformation conditions reach 13.9 GPa and 12.5 GPa when the strains are 0.07 and 0.28,respectively.The folded five-membered rings and diverse bonding modes between carbon and nitrogen atoms enhance the ability to resist plastic deformation of C_(4)N_(4).The orderly bond-rearranging behaviors under the weak tensile loading path along the[100]direction cause the impressive semiconductor–metal transition and inverse semiconductor–metal transition.The present results enrich the knowledge of the structure and electronic properties of C_(4)N_(4)under deformations and shed light on exploring other two-dimensional materials under diverse loading conditions.
基金supported by the Shenzhen Basic Research Project,No.JCYJ20190807155805818the Foundation of Guangdong Provincial Key Laboratory of Sensor Technology and Biomedical Instrument,No.2020B1212060077the Sun Yat-sen University Training Program of Research for Undergraduates,No.76190-51200001.
文摘Background:Excessive exudate secreted from chronic wounds often leads to overhydration and infection.Although a variety of dressings are currently available in clinical applications,they frequently fail to provide multifunction to promote chronic wound healing.The dressings with a Janus structure,featuring distinct properties on each side,are potential to improve wound healing.Methods:Composite dressings with a Janus structure were fabricated,comprising freeze-dried polycaprolactone(PCL)electrospun membrane and alginate-based hydrogel.The PCL fibrous membrane provided air permeability,while the hydrogel loaded with Deferoxamine,composed of alginate and poly(N-isopropylacrylamide)(PNIPAM),exhibited hygroscopic properties.The inclusion of PNIPAM imparted thermo-responsivity.Results:The hydrogel(thickness of 2.778±0.082 mm)exhibited a robust adhesion to the fiber membrane(thickness of 0.261±0.041 mm).For ANDC(Alginate-PNIPAM hydrogel with Deferoxamine/PCL membrane)samples,the water vapor transmission rate(WVTR)was measured to be 3364.80±23.23 g∙m−2∙day−1 and the swelling ratio at 2 h was determined to be 1179±125%.The thermo-responsivity of ANDC samples manifested in an increased swelling rate,escalating from 797±189%at 37°C to 1132±147%at 4°C.The elastic modulus was assessed for lyophilized and rehydrated ANDC sample.When theωof the rheometer rotor was decreased from 10 rad/s to 0.1 rad/s,the lyophilized dressing exhibited a decrease from 2.65±0.01 MPa to 1.80±0.90 MPa,while the rehydrated dressing demonstrated an increase from 133.65±55.68 Pa to 264.23±141.71 Pa.The pro-healing properties of the dressings were evaluated using full-thickness skin defect model on SD rats,and a circular wound of diameter 10 mm healed completely by day 12.Conclusion:The dressings not only protected the wound and absorbed excess exudate,but also demonstrated nondestructive peelability upon cooling,providing a novel approach for accelerating wound healing and management.
基金Project supported by the Shanghai Nanoscience Foundation,China (Grant Nos. 0852nm07000 and 0952nm07000)the National Natural Science Foundation of China (Grant Nos. 10804084 and 91123022)+1 种基金the National Key Technology R & D Program,China (Grant No. 2006BAF06B08)the Specialized Research Fund for the Doctoral Program of Ministry of High Education of China (Grant No. 200802471008)
文摘Direct-write atom lithography,one of the potential nanofabrication techniques,is restricted by some difficulties in producing optical masks for the deposition of complex structures.In order to make further progress,a structured mirror array is developed to transversely collimate the chromium atomic beam in two dimensions.The best collimation is obtained when the laser red detunes by natural line-width of transition 7S3 → 7P40 of the chromium atom.The collimation ratio is 0.45 vertically（in x axis）,and it is 0.55 horizontally（in y axis）.The theoretical model is also simulated,and success of our structured mirror array is achieved.
基金the Hong Kong Scholar Program (XJ2018035) for their financial supportsupported by Research Grants Council of Hong Kong (No. JLFS/E-402/18)National Natural Science Foundation of China (No. 51805509)。
文摘Several natural organism can change shape under external stimuli. These natural phenomena have inspired a vast amount of research on exploration and implementation of reconfigurable shape transformation. The Janus structure is a promising approach to achieve shape transformation based on its heterogeneous chemical or physical properties on opposite sides.However, the heterogeneity is generally realized by multi-step processing, different materials,and/or different processing parameters. Here, we present a simple and flexible method of producing p H-sensitive Janus microactuators from a single material, using the same laser printing parameters. These microactuators exhibit reversible structural deformations with large bending angles of ~31°and fast response(~0.2 s) by changing the p H value of the aqueous environment. Benefited from the high flexibility of the laser printing technique and the spatial arrangements, pillar heights, and bending directions of microactuators are readily controlled,enabling a variety of switchable ordered patterns and complex petal-like structures on flat surfaces and inside microchannels. Finally, we explore the potential applications of this method in information encryption/decryption and microtarget capturing.
基金Project supported by the National Natural Science Foundations of China(Grant No.61275047)the Research Project of Chinese Ministry of Education(Grant No.213009A)the Scientific and Technological Development Foundation of Jilin Province,China(Grant No.20130101031JC)
文摘Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic crystals for TE and TM waves are different from the two-dimensional conventional photonic crystals. Some absolute band gaps and semiDirac points are found. When the medium column radius and the function form of the dielectric constant are modulated, the numbers, width, and position of band gaps are changed, and the semi-Dirac point can either occur or disappear. Therefore,the special band gaps structures and semi-Dirac points can be achieved through the modulation on the two-dimensional function photonic crystals. The results will provide a new design method of optical devices based on the two-dimensional function photonic crystals.
文摘The algebraic solitary wave and its associated eigenvalue problem in a deep stratified fluid with a free surface and a shallow upper layer were studied. And its vertical structure was examined. An exact solution for the derived 2D Benjamin-Ono equation was obtained, and physical explanation was given with the corresponding dispersion relation. As a special case, the vertical structure of the weakly nonlinear internal wave for the Holmboe density distribution was numerically investigated, and the propagating mechanism of the internal wave was studied by using the ray theory.
基金the National Research and Development Program of China(Grant Nos.2016YFA0300503 and 2017YFA0302900)the National Natural Science Foundation of China(Grant Nos.12274458,11774420,and 11974194)the Research Funds of Renmin University of China(Grant No.20XNLG19).
文摘Two-dimensional(2D)magnetic materials have attracted tremendous research interest because of the promising application in the next-generation microelectronic devices.Here,by the first-principles calculations,we propose a twodimensional ferromagnetic material with high Curie temperature,manganese tetranitride MnN4monolayer,which is a square-planar lattice made up of only one layer of atoms.The structure is demonstrated to be stable by the phonon spectra and the molecular dynamic simulations,and the stability is ascribed to theπ–d conjugation betweenπorbital of N=N bond and d orbital of Mn.More interestingly,the MnN_(4)monolayer displays robust 2D ferromagnetism,which originates from the strong exchange couplings between Mn atoms due to theπ–d conjugation.The high critical temperature of 247 K is determined by solving the Heisenberg model using the Monte Carlo method.
基金Project supported by the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20190736)the Young Scientists Fund of the National Natural Science Foundation of China(Grant Nos.81701346 and 61603198)Qinglan Team of Universities in Jiangsu Province(Jiangsu Teacher Letter[2020]10 and Jiangsu Teacher Letter[2021]11).
文摘Characterizing the trajectory of the healthy aging brain and exploring age-related structural changes in the brain can help deepen our understanding of the mechanism of brain aging.Currently,most structural magnetic resonance imaging literature explores brain aging merely from the perspective of morphological features,which cannot fully utilize the grayscale values containing important intrinsic information about brain structure.In this study,we propose the construction of two-dimensional horizontal visibility graphs based on the pixel intensity values of the gray matter slices directly.Normalized network structure entropy(NNSE)is then introduced to quantify the overall heterogeneities of these graphs.The results demonstrate a decrease in the NNSEs of gray matter with age.Compared with the middle-aged and the elderly,the larger values of the NNSE in the younger group may indicate more homogeneous network structures,smaller differences in importance between nodes and thus a more powerful ability to tolerate intrusion.In addition,the hub nodes of different adult age groups are primarily located in the precuneus,cingulate gyrus,superior temporal gyrus,inferior temporal gyrus,parahippocampal gyrus,insula,precentral gyrus and postcentral gyrus.Our study can provide a new perspective for understanding and exploring the structural mechanism of brain aging.
基金supported by the Hainan Provincial Natural Science Foundation of China(222RC548)the National Natural Science Foun-dation of China(22109034,22109035,52164028,62105083,21805104)+3 种基金the Opening Project of Key Laboratory of Electrochemical Energy Storage and Energy Conversion of Hainan Province(KFKT2021007)the Start-up Research Foundation of Hainan University(KYQD(ZR)-20008,20082,20083,20084,21065,21124,21125)the Innovative Research Projects for Graduate Students of Hainan Province(Qhyb2022-89,Qhys2022-174)the State Key Laboratory of Powder Metallurgy,Central South University,Changsha,China and the Specific Research Fund of the Innovation Platform for Academicians of Hainan Province.
文摘Electrocatalytic CO_(2) reduction reaction(eCO_(2) RR)has significant relevance to settle the global energy crisis and abnormal climate problem via mitigating the excess emission of waste CO_(2) and producing high-value-added chemicals.Currently,eCO_(2) RR to formic acid or formate is one of the most technologically and economically viable approaches to realize high-efficiency CO_(2) utilization,and the development of efficient electrocatalysts is very urgent to achieve efficient and stable catalytic performance.In this review,the recent advances for two-dimensional bismuth-based nanosheets(2D Bi-based NSs)electrocatalysts are concluded from both theoretical and experimental perspectives.Firstly,the preparation strategies of 2D Bi-based NSs in aspects to precisely control the thickness and uniformity are summarized.In addition,the electronic regulation strategies of 2D Bi-based NSs are highlighted to gain insight into the effects of the structure-property relationship on facilitating CO_(2) activation,improving product selectivity,and optimizing carrier transport dynamics.Finally,the considerable challenges and opportunities of 2D Bi-based NSs are discussed to lighten new directions for future research of eCO_(2) RR.
基金The research of Gui-Qiang G.Chen was supported in part by the UK Engineering and Physical Sciences Research Council Awards EP/L015811/1,EP/V008854/1,EP/V051121/1the Royal Society-Wolfson Research Merit Award WM090014.
文摘We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.
基金supported by the National Natural Science Foundation of China(21878062)the Natural Science Foundation of Heilongjiang Province for Distinguished Young Scholars(JQ2020B001)+1 种基金Heilongjiang Touyan Team(HITTY-20190033)Open Project of State Key Laboratory of Urban Water Resource and Environment(Harbin Institute of Technology)(QA202127)。
