An improved algorithm for computing multiphase flows is presented in which the multimaterial Moment-of-Fluid(MOF)algorithm for multiphase flows,initially described by Li et al.(2015),is enhanced addressing existing MO...An improved algorithm for computing multiphase flows is presented in which the multimaterial Moment-of-Fluid(MOF)algorithm for multiphase flows,initially described by Li et al.(2015),is enhanced addressing existing MOF difficulties in computing solutions to problems in which surface tension forces are crucial for understanding salient flow mechanisms.The Continuous MOF(CMOF)method is motivated in this article.The CMOF reconstruction method inherently removes the"checkerboard instability"that persists when using the MOF method on surface tension driven multiphase(multimaterial)flows.The CMOF reconstruction algorithm is accelerated by coupling the CMOF method to the level set method and coupling the CMOF method to a decision tree machine learning(ML)algorithm.Multiphase flow examples are shown in the two-dimensional(2D),three-dimensional(3D)axisymmetric"RZ",and 3D coordinate systems.Examples include two material and three material multiphase flows:bubble formation,the impingement of a liquid jet on a gas bubble in a cryogenic fuel tank,freezing,and liquid lens dynamics.展开更多
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a...This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.展开更多
This article considers the existence of solution for a boundary value problem of fractional order, involving Caputo's derivative{C0D^δtu(t)=g(t,u(t)),0〈t〈1,1〈δ〈2,u(0)α≠0,u(1)=β≠0.
This paper is concerned with the boundary value problem of a nonlinear fractional differential equation. By means of Schauder fixed-point theorem, an existence result of solution is obtained.
In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q (1 〈 q 〈 2) with non-separated integral boundary conditions. Some new existence and uniqueness results a...In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q (1 〈 q 〈 2) with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.展开更多
Based on Biot’s theory and considering the properties of a cavity,the boundary integral equations for the numerical simulation of wave scattering around a cavity with a circular cross-section embedded in saturated so...Based on Biot’s theory and considering the properties of a cavity,the boundary integral equations for the numerical simulation of wave scattering around a cavity with a circular cross-section embedded in saturated soil are obtained using integral transform methods.The Cauchy type singularity of the boundary integral equation is discussed.The effectiveness of the properties of soil mass and incident field on the dynamic stress concentration and pore pressure concentration around a cavity is analyzed.Our results are in good agreement with the existing solution.The numerical results of this work show that the dynamic stress concentration and pore pressure concentration are influenced by the degree of fluid–solid coupling as well as the pore compressibility and water permeability of saturated soil.With increased degree of fluid–solid coupling,the dynamic stress concentration improves from 1.87 to 3.42 and the scattering becomes more significant.With decreased index of soil mass compressibility,the dynamic stress concentration increases and its maximum reaches 3.67.The dynamic stress concentration increases from 1.64 to 3.49 and pore pressure concentration improves from 0.18 to 0.46 with decreased water permeability of saturated soil.展开更多
The present note is concerned with two connected and highly important fundamental questions of physics and cosmology, namely if E8E8 Lie symmetry group describes the universe and where cosmic dark energy comes from. F...The present note is concerned with two connected and highly important fundamental questions of physics and cosmology, namely if E8E8 Lie symmetry group describes the universe and where cosmic dark energy comes from. Furthermore, we reason following Wheeler, Hartle and Hawking that since the boundary of a boundary is an empty set which models the quantum wave of the cosmos, then it follows that dark energy is a fundamental physical phenomenon associated with the boundary of the holographic boundary. This leads directly to a clopen universe which is its own Penrose tiling-like multiverse with energy density in full agreement with COBE, WMAP and Type 1a supernova cosmic measurements.展开更多
The present work studied the corrosion properties around the fusion boundaries of 2.25Cr-1Mo steel with stainless steel strip overlay joints under as welded condition and after post-weld heat treatment (PWHT) in H2 S ...The present work studied the corrosion properties around the fusion boundaries of 2.25Cr-1Mo steel with stainless steel strip overlay joints under as welded condition and after post-weld heat treatment (PWHT) in H2 S containing solution (NACE TM-01-77 standard) with different time. An in-situ observation method was introduced for evaluating corrosive progress in the fusion boundary in H2 S containing solution, that is, the samples were marked firstly at the boundary and then treated in the solution for variant time. Each time after the corrosion treatment, the observations were kept to focus at the same marked area by using scanning electron microscopy (SEM) to observe the corrosion progress. The results reveal that the fusion boundary is the worst region for corrosion resistance when comparing with other boundaries, and a broad fusion boundary has a stronger resistance for "hydrogen induced disbonding" than a narrow one.展开更多
In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green's function for this problem and show that it satisfies certain propertie...In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green's function for this problem and show that it satisfies certain properties. Some existence results are obtained by means of nonlinear alternative of Leray-Schauder type theorem and Krasnosel-skii's fixed point theorem.展开更多
The alternating method based on the fundamental solutions of the infinite domain containing a crack,namely Muskhelishvili’s solutions,divides the complex structure with a crack into a simple model without crack which...The alternating method based on the fundamental solutions of the infinite domain containing a crack,namely Muskhelishvili’s solutions,divides the complex structure with a crack into a simple model without crack which can be solved by traditional numerical methods and an infinite domain with a crack which can be solved by Muskhelishvili’s solutions.However,this alternating method cannot be directly applied to the edge crack problems since partial crack surface of Muskhelishvili’s solutions is located outside the computational domain.In this paper,an improved alternating method,the spline fictitious boundary element alternating method(SFBEAM),based on infinite domain with the combination of spline fictitious boundary element method(SFBEM)and Muskhelishvili’s solutions is proposed to solve the edge crack problems.Since the SFBEM and Muskhelishvili’s solutions are obtained in the framework of infinite domain,no special treatment is needed for solving the problem of edge cracks.Different mixed boundary conditions edge crack problems with varies of computational parameters are given to certify the high precision,efficiency and applicability of the proposed method compared with other alternating methods and extend finite element method.展开更多
Anew artificial boundary model based on multi-directional transmitting and viscous-spring artificial boundary theories is proposed to absorb stress waves in a saturated soil foundation in dynamic analysis. Since shear...Anew artificial boundary model based on multi-directional transmitting and viscous-spring artificial boundary theories is proposed to absorb stress waves in a saturated soil foundation in dynamic analysis. Since shear waves (S-waves) are the same in a saturated soil foundation and a single-phase medium foundation, a tangential visco-elastic boundary condition for a single-phase medium foundation can also be used for saturated soil foundations. Thus, the purpose of the artificial boundary proposed in this paper is primarily to absorb two types of P-waves in a saturated soil foundation. The main idea is that the stress of the P-waves in the saturated soil foundation is decomposed into two types. The first type of stress, δra' is absorbed by the first artificial boundary. The second type of stress, δrb, is balanced by the stress generated by the second artificial boundary. Ultimately, both types of P-waves (fast-P-waves and slow-P-waves) are absorbed by the artificial boundary model proposed in this paper. In particular, note that the fast-P-waves and slow-P-waves are absorbed at the position of the first boundary. Thus, the artificial boundary model proposed herein can simultaneously absorb P-fast waves, P-slow waves and shear waves. Finally, a numerical example is given to examine the proposed artificial boundary model, and the results show that it is very accurate.展开更多
According to a series of important historical maps,i.e.,the Location Map of the South China Sea Islands,the Nansha Islands,Zhongsha Islands,Xisha Islands,Yongxing Island and Shidao Island,and Taiping Island(archived ...According to a series of important historical maps,i.e.,the Location Map of the South China Sea Islands,the Nansha Islands,Zhongsha Islands,Xisha Islands,Yongxing Island and Shidao Island,and Taiping Island(archived by the Territorial Administration Division of the Ministry of Interior of Republic of China in 1946),and the Administration District Map of the Republic of China published in 1948,the dashed line surrounding the South China Sea Islands represents China's sea boundary in the South China Sea at that time.It was both connected with,and an extension of,the land boundary of China.At that time the dashed line was used to represent the waters boundaries while the solid line was used to represent the land boundary—a universal method used in maps that was then recognized internationally.The above observation provides historical and scientific evidence of China's sea boundary in the South China Sea that is useful for the international maritime delimitation over the South China Sea area.展开更多
The possibility of using Neumann's method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the...The possibility of using Neumann's method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the distribution space. The convergence of Neumann's method is proven for the shells with holes when the boundary of the domain is not completely fixed. The numerical implementation of Neumann's method normally requires significant time before any reliable results can be achieved. This paper suggests a way to improve the convergence of the process, and allows for parallel computing and evaluation during the calculations.展开更多
By using Leray-Schauder nonlinear alternative, Banach contraction theorem and Guo-Krasnosel’skii theorem, we discuss the existence, uniqueness and positivity of solution to the third-order multi-point nonhomogeneous ...By using Leray-Schauder nonlinear alternative, Banach contraction theorem and Guo-Krasnosel’skii theorem, we discuss the existence, uniqueness and positivity of solution to the third-order multi-point nonhomogeneous boundary value problem (BVP1): where for The interesting point lies in the fact that the nonlinear term is allowed to depend on the first order derivative .展开更多
The existence and multiplicity of positive solutions are studied for a class of quasi- linear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational...The existence and multiplicity of positive solutions are studied for a class of quasi- linear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational methods and some analytical techniques.展开更多
In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α+u(t)+f(t,u(t),u'(t),…,u^(n-3)(5),u^(n-2)(t))=0,u^(i)(0)=0,0≤i≤n-2,u^(n-...In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α+u(t)+f(t,u(t),u'(t),…,u^(n-3)(5),u^(n-2)(t))=0,u^(i)(0)=0,0≤i≤n-2,u^(n-2)(1)-βu^(n-2)(ξ)=0,where 0〈t〈1,n-1〈α≤n,n≥2,ξ Е(0,1),βξ^a-n〈1. We first transform it into another equivalent boundary value problem. Then, we derive the Green's function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result.展开更多
There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle th...There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace’s equation (or Helmholtz equation) arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.展开更多
基金supported by the National Aeronautics and Space Administration under grant number 80NSSC20K0352.
文摘An improved algorithm for computing multiphase flows is presented in which the multimaterial Moment-of-Fluid(MOF)algorithm for multiphase flows,initially described by Li et al.(2015),is enhanced addressing existing MOF difficulties in computing solutions to problems in which surface tension forces are crucial for understanding salient flow mechanisms.The Continuous MOF(CMOF)method is motivated in this article.The CMOF reconstruction method inherently removes the"checkerboard instability"that persists when using the MOF method on surface tension driven multiphase(multimaterial)flows.The CMOF reconstruction algorithm is accelerated by coupling the CMOF method to the level set method and coupling the CMOF method to a decision tree machine learning(ML)algorithm.Multiphase flow examples are shown in the two-dimensional(2D),three-dimensional(3D)axisymmetric"RZ",and 3D coordinate systems.Examples include two material and three material multiphase flows:bubble formation,the impingement of a liquid jet on a gas bubble in a cryogenic fuel tank,freezing,and liquid lens dynamics.
文摘This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.
基金Supported by the National 973-Project from MOST and Trans-Century Training Programme Foundation for the Talents by Ministry of Education and the Postdoctoral Foundation of China.
文摘This article considers the existence of solution for a boundary value problem of fractional order, involving Caputo's derivative{C0D^δtu(t)=g(t,u(t)),0〈t〈1,1〈δ〈2,u(0)α≠0,u(1)=β≠0.
文摘This paper is concerned with the boundary value problem of a nonlinear fractional differential equation. By means of Schauder fixed-point theorem, an existence result of solution is obtained.
文摘In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q (1 〈 q 〈 2) with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.
基金Projects(50969007,51269021) supported by the National Natural Science Foundation of ChinaProjects(20114BAB206012,20133ACB20006) supported by the Natural Science Foundation of Jiangxi Province of China
文摘Based on Biot’s theory and considering the properties of a cavity,the boundary integral equations for the numerical simulation of wave scattering around a cavity with a circular cross-section embedded in saturated soil are obtained using integral transform methods.The Cauchy type singularity of the boundary integral equation is discussed.The effectiveness of the properties of soil mass and incident field on the dynamic stress concentration and pore pressure concentration around a cavity is analyzed.Our results are in good agreement with the existing solution.The numerical results of this work show that the dynamic stress concentration and pore pressure concentration are influenced by the degree of fluid–solid coupling as well as the pore compressibility and water permeability of saturated soil.With increased degree of fluid–solid coupling,the dynamic stress concentration improves from 1.87 to 3.42 and the scattering becomes more significant.With decreased index of soil mass compressibility,the dynamic stress concentration increases and its maximum reaches 3.67.The dynamic stress concentration increases from 1.64 to 3.49 and pore pressure concentration improves from 0.18 to 0.46 with decreased water permeability of saturated soil.
文摘The present note is concerned with two connected and highly important fundamental questions of physics and cosmology, namely if E8E8 Lie symmetry group describes the universe and where cosmic dark energy comes from. Furthermore, we reason following Wheeler, Hartle and Hawking that since the boundary of a boundary is an empty set which models the quantum wave of the cosmos, then it follows that dark energy is a fundamental physical phenomenon associated with the boundary of the holographic boundary. This leads directly to a clopen universe which is its own Penrose tiling-like multiverse with energy density in full agreement with COBE, WMAP and Type 1a supernova cosmic measurements.
文摘The present work studied the corrosion properties around the fusion boundaries of 2.25Cr-1Mo steel with stainless steel strip overlay joints under as welded condition and after post-weld heat treatment (PWHT) in H2 S containing solution (NACE TM-01-77 standard) with different time. An in-situ observation method was introduced for evaluating corrosive progress in the fusion boundary in H2 S containing solution, that is, the samples were marked firstly at the boundary and then treated in the solution for variant time. Each time after the corrosion treatment, the observations were kept to focus at the same marked area by using scanning electron microscopy (SEM) to observe the corrosion progress. The results reveal that the fusion boundary is the worst region for corrosion resistance when comparing with other boundaries, and a broad fusion boundary has a stronger resistance for "hydrogen induced disbonding" than a narrow one.
基金Supported by the National Natural Science Foundation of China(11161049)
文摘In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green's function for this problem and show that it satisfies certain properties. Some existence results are obtained by means of nonlinear alternative of Leray-Schauder type theorem and Krasnosel-skii's fixed point theorem.
基金supported by the National Natural Science Foundation of China(51078150)the National Natural Science Foundation of China(11602087)+1 种基金the State Key Laboratory of Subtropical Building Science,South China University of Technology(2017ZB32)National Undergraduate Innovative and Entrepreneurial Training Program(201810561180).
文摘The alternating method based on the fundamental solutions of the infinite domain containing a crack,namely Muskhelishvili’s solutions,divides the complex structure with a crack into a simple model without crack which can be solved by traditional numerical methods and an infinite domain with a crack which can be solved by Muskhelishvili’s solutions.However,this alternating method cannot be directly applied to the edge crack problems since partial crack surface of Muskhelishvili’s solutions is located outside the computational domain.In this paper,an improved alternating method,the spline fictitious boundary element alternating method(SFBEAM),based on infinite domain with the combination of spline fictitious boundary element method(SFBEM)and Muskhelishvili’s solutions is proposed to solve the edge crack problems.Since the SFBEM and Muskhelishvili’s solutions are obtained in the framework of infinite domain,no special treatment is needed for solving the problem of edge cracks.Different mixed boundary conditions edge crack problems with varies of computational parameters are given to certify the high precision,efficiency and applicability of the proposed method compared with other alternating methods and extend finite element method.
基金National Natural Science Foundation of China Under Grant Nos.51109029,51178081,51138001,51009020China Postdoctoral Science Foundation Under Grant No. 20110491535
文摘Anew artificial boundary model based on multi-directional transmitting and viscous-spring artificial boundary theories is proposed to absorb stress waves in a saturated soil foundation in dynamic analysis. Since shear waves (S-waves) are the same in a saturated soil foundation and a single-phase medium foundation, a tangential visco-elastic boundary condition for a single-phase medium foundation can also be used for saturated soil foundations. Thus, the purpose of the artificial boundary proposed in this paper is primarily to absorb two types of P-waves in a saturated soil foundation. The main idea is that the stress of the P-waves in the saturated soil foundation is decomposed into two types. The first type of stress, δra' is absorbed by the first artificial boundary. The second type of stress, δrb, is balanced by the stress generated by the second artificial boundary. Ultimately, both types of P-waves (fast-P-waves and slow-P-waves) are absorbed by the artificial boundary model proposed in this paper. In particular, note that the fast-P-waves and slow-P-waves are absorbed at the position of the first boundary. Thus, the artificial boundary model proposed herein can simultaneously absorb P-fast waves, P-slow waves and shear waves. Finally, a numerical example is given to examine the proposed artificial boundary model, and the results show that it is very accurate.
文摘According to a series of important historical maps,i.e.,the Location Map of the South China Sea Islands,the Nansha Islands,Zhongsha Islands,Xisha Islands,Yongxing Island and Shidao Island,and Taiping Island(archived by the Territorial Administration Division of the Ministry of Interior of Republic of China in 1946),and the Administration District Map of the Republic of China published in 1948,the dashed line surrounding the South China Sea Islands represents China's sea boundary in the South China Sea at that time.It was both connected with,and an extension of,the land boundary of China.At that time the dashed line was used to represent the waters boundaries while the solid line was used to represent the land boundary—a universal method used in maps that was then recognized internationally.The above observation provides historical and scientific evidence of China's sea boundary in the South China Sea that is useful for the international maritime delimitation over the South China Sea area.
文摘The possibility of using Neumann's method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the distribution space. The convergence of Neumann's method is proven for the shells with holes when the boundary of the domain is not completely fixed. The numerical implementation of Neumann's method normally requires significant time before any reliable results can be achieved. This paper suggests a way to improve the convergence of the process, and allows for parallel computing and evaluation during the calculations.
文摘By using Leray-Schauder nonlinear alternative, Banach contraction theorem and Guo-Krasnosel’skii theorem, we discuss the existence, uniqueness and positivity of solution to the third-order multi-point nonhomogeneous boundary value problem (BVP1): where for The interesting point lies in the fact that the nonlinear term is allowed to depend on the first order derivative .
基金Supported by National Natural Science Foundation of China (11071198 11101347)+2 种基金Postdoctor Foundation of China (2012M510363)the Key Project in Science and Technology Research Plan of the Education Department of Hubei Province (D20112605 D20122501)
文摘The existence and multiplicity of positive solutions are studied for a class of quasi- linear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational methods and some analytical techniques.
基金Supported by the National Nature Science Foundation of China(11071001)Supported by the Key Program of Ministry of Education of China(205068)
文摘In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α+u(t)+f(t,u(t),u'(t),…,u^(n-3)(5),u^(n-2)(t))=0,u^(i)(0)=0,0≤i≤n-2,u^(n-2)(1)-βu^(n-2)(ξ)=0,where 0〈t〈1,n-1〈α≤n,n≥2,ξ Е(0,1),βξ^a-n〈1. We first transform it into another equivalent boundary value problem. Then, we derive the Green's function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result.
文摘There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace’s equation (or Helmholtz equation) arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.