The mathematical physics model of mine methane and coal dust explosion propagation was established in the research,by using continuous phase,combustion,par- ticulate equations of mathematical physics.Based upon the da...The mathematical physics model of mine methane and coal dust explosion propagation was established in the research,by using continuous phase,combustion,par- ticulate equations of mathematical physics.Based upon the data from mine methane drainage roadway explosion,and mine methane and coal dust explosion propagation ex- perimental studies,the numerical emulator system of mine methane and coal dust explo- sion software was developed by using prevalent flow simulation platform,which can be used to simulate the explosion accidents process effectively.In addition,the system can also be used to determine whether coal dust involved in the explosion,and to simulate accurately the transition from deflagration to detonation in methane explosion,propagation velocity of explosion shock,attenuation pattern,and affected area of explosion.展开更多
In this paper,an efficient fully-decoupled and fully-discrete numerical scheme with second-order temporal accuracy is developed to solve the incompressible hydrodynamically coupled Cahn-Hilliard model for simulating t...In this paper,an efficient fully-decoupled and fully-discrete numerical scheme with second-order temporal accuracy is developed to solve the incompressible hydrodynamically coupled Cahn-Hilliard model for simulating the two-phase fluid flow system.The scheme is developed by combining the finite element method for spatial discretization and several effective time marching approaches,including the pressure-correction projection method for dealing with fluid equations and the explicit-invariant energy quadratization(explicit-IEQ)approach for dealing with coupled nonlinear terms.The obtained scheme is very efficient since it only needs to solve several decoupled,linear elliptic equations with constant coefficients at each time step.We also strictly prove the solvability and unconditional energy stability of the scheme,and verify the accuracy and stability of the scheme through plenty of numerical examples.展开更多
Fluid flow at nanoscale is closely related to many areas in nature and technology(e.g.,unconventional hydrocarbon recovery,carbon dioxide geo-storage,underground hydrocarbon storage,fuel cells,ocean desalination,and b...Fluid flow at nanoscale is closely related to many areas in nature and technology(e.g.,unconventional hydrocarbon recovery,carbon dioxide geo-storage,underground hydrocarbon storage,fuel cells,ocean desalination,and biomedicine).At nanoscale,interfacial forces dominate over bulk forces,and nonlinear effects are important,which significantly deviate from conventional theory.During the past decades,a series of experiments,theories,and simulations have been performed to investigate fluid flow at nanoscale,which has advanced our fundamental knowledge of this topic.However,a critical review is still lacking,which has seriously limited the basic understanding of this area.Therefore herein,we systematically review experimental,theoretical,and simulation works on single-and multi-phases fluid flow at nanoscale.We also clearly point out the current research gaps and future outlook.These insights will promote the significant development of nonlinear flow physics at nanoscale and will provide crucial guidance on the relevant areas.展开更多
To improve the accuracy of the conventional finite-difference method, finitedifference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of ...To improve the accuracy of the conventional finite-difference method, finitedifference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of any-order derivatives derived from Taylor series expansion. Then, a finite-difference numerical modeling method with any evenorder accuracy is utilized to simulate seismic wave propagation in two-phase anisotropic media. Results indicate that modeling accuracy improves with the increase of difference accuracy order number. It is essential to find the optimal order number, grid size, and time step to balance modeling precision and computational complexity. Four kinds of waves, static mode in the source point, SV wave cusps, reflection and transmission waves are observed in two-phase anisotropic media through modeling.展开更多
The fundamental equations of multiphase flow that have been established so far fall into two main groups, the multifluid model and the mixture model [1] [2]. Because of the different forms of the equations derived fro...The fundamental equations of multiphase flow that have been established so far fall into two main groups, the multifluid model and the mixture model [1] [2]. Because of the different forms of the equations derived from these two models, many disputes arose [1] [3] [4]. This paper deals mainly with the basic principles for establishing the fundamental equations of multiphase flow, namely the principles of consistency, invariance of material coordinates and material indifference. The results lead to the consistent description of the two models.展开更多
The modulation instability （MI） induced by cross-phase modulation （XPM） in dispersion-decreasing fiber （DDF）, whose dispersion decreases along the direction of propagation, is solved and analyzed by the pertur- ...The modulation instability （MI） induced by cross-phase modulation （XPM） in dispersion-decreasing fiber （DDF）, whose dispersion decreases along the direction of propagation, is solved and analyzed by the pertur- bation method for the extended nonlinear SchrSdinger equation, considering the higher-order dispersion. The change of the gain spectra with incident power and dispersion decaying factor are also given respec- tively. Due to the fourth-order dispersion, XPM occurs at two gain spectral regions in both the normal and the anomalous dispersion regimes of DDF. The two gain spectral regions in the anomalous dispersion regime are larger than those in the normal dispersion ond region in the anomalous dispersion regime is near regime. Moreover, the gain spectrum of the sec- zero compared with that in the normal dispersion regime, indicating that XPM can be easily produced in the anomalous dispersion regime. The spectral width increases with the increase of the incident optical power and the dispersion decaying factor.展开更多
This article describes mathematical models for phase separated mixtures of materials that are in pressure and velocity equilibrium but not necessarily temperature equilibrium. General conditions for constitutive model...This article describes mathematical models for phase separated mixtures of materials that are in pressure and velocity equilibrium but not necessarily temperature equilibrium. General conditions for constitutive models for such mixtures that exhibit a single mixture sound speed are discussed and specific examples are described.展开更多
Abstract.In this paper,a novel implementation of immersed interface method combined with Stokes solver on a MAC staggered grid for solving the steady two-fluid Stokes equations with interfaces.The velocity components ...Abstract.In this paper,a novel implementation of immersed interface method combined with Stokes solver on a MAC staggered grid for solving the steady two-fluid Stokes equations with interfaces.The velocity components along the interface are introduced as two augmented variables and the resulting augmented equation is then solved by the GMRES method.The augmented variables and/or the forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity,and are interpolated using cubic splines and are then applied to the fluid through the jump conditions.The Stokes equations are discretized on a staggered Cartesian grid via a second order finite difference method and solved by the conjugate gradient Uzawa-typemethod.The numerical results show that the overall scheme is second order accurate.The major advantages of the present IIM-Stokes solver are the efficiency and flexibility in terms of types of fluid flow and different boundary conditions.The proposed method avoids solution of the pressure Poisson equation,and comparisons are made to show the advantages of time savings by the present method.The generalized two-phase Stokes solver with correction terms has also been applied to incompressible two-phase Navier-Stokes flow.展开更多
A century ago the classical physics couldn’t explain many atomic physical phenomena. Now the situation has changed. It’s because within the framework of classical physics with the help of Maxwell’s equations we can...A century ago the classical physics couldn’t explain many atomic physical phenomena. Now the situation has changed. It’s because within the framework of classical physics with the help of Maxwell’s equations we can derive Schrödinger’s equation, which is the foundation of quantum physics. The equations for energy, momentum, frequency and wavelength of the electromagnetic wave in the atom are derived using the model of atom by analogy with the transmission line. The action constant A0 = (μ0/ε0)1/2s02e2 is a key term in the above mentioned equations. Besides the other well-known constants, the only unknown constant in the last expression is a structural constant of the atom s0. We have found that the value of this constant is 8.277 56 and that it shows up as a link between macroscopic and atomic world. After calculating this constant we get the theory of atoms based on Maxwell’s and Lorentz equations only. This theory does not require knowledge of Planck’s constant h, which is replaced with theoretically derived action constant A0, while the replacement for the fine structure constant α-1 is theoretically derived expression 2s02 = 137.036. So, the structural constant s0 replaces both constants h and α. This paper also defines the stationary states of atoms and shows that the maximal atomic number is equal to Zmax = 137. The presented model of the atoms covers three of the four fundamental interactions, namely the electromagnetic, weak and strong interactions.展开更多
In this research article, we investigate the stability of a complex dynamical system involving coupled rigid bodies consisting of three equal masses joined by three rigid rods of equal lengths, hinged at each of their...In this research article, we investigate the stability of a complex dynamical system involving coupled rigid bodies consisting of three equal masses joined by three rigid rods of equal lengths, hinged at each of their bases. The system is free to oscillate in the vertical plane. We obtained the equation of motion using the generalized coordinates and the Euler-Lagrange equations. We then proceeded to study the stability of the dynamical systems using the Jacobian linearization method and subsequently confirmed our result by phase portrait analysis. Finally, we performed MathCAD simulation of the resulting ordinary differential equations, describing the dynamics of the system and obtained the graphical profiles for each generalized coordinates representing the angles measured with respect to the vertical axis. It is discovered that the coupled rigid pendulum gives rise to irregular oscillations with ever increasing amplitude. Furthermore, the resulting phase portrait analysis depicted spiral sources for each of the oscillating masses showing that the system under investigation is unstable.展开更多
The main features are the length of the waveguide in one direction, as well as limitations and localization of the wave beam in other areas. There is described the technique of the solution of tasks on distribution of...The main features are the length of the waveguide in one direction, as well as limitations and localization of the wave beam in other areas. There is described the technique of the solution of tasks on distribution of waves in an infinite cylindrical waveguide with a radial crack. Also numerical results are given in the article. Viscous properties of the material are taken into account by means of an integral operator Voltaire. Research is conducted in the framework of the spatial theory of visco elastic. The technique is based on the separation of spatial variables and formulates the boundary eigenvalue problem that can be solved by the method of orthogonal sweep Godunov. In the given paper we obtain numeric values of the phase velocity depending on of wave numbers. The obtained numerical results are compared with the known data. This work is continuation of article [1]. Statement of the problem and methodology of partial solutions are described in [1]. In this work, we present a complete statement of the problem, methods of solution and discuss the numerical results.展开更多
Here we review a new class of mixing rules (hat have extended range of mixtures and conditions that can now be described by equation of state models. One characteristic of these mixing rules is that they simultaneousl...Here we review a new class of mixing rules (hat have extended range of mixtures and conditions that can now be described by equation of state models. One characteristic of these mixing rules is that they simultaneously satisfy the boundary conditions of producing a second virial coefficient that is quadratic in mole fraction, and a free energy of mixing like that of an activity coefficient model at high density, though the mixing rule is itself independent of density. We show that using this mixing rule, various asymmetric, highly nonideal mixtures can be accurately described. One serendipitous result is that the parameters in this mixing rule model are almost independent of temperature, which allows accurate extrapolations of phase behavior to be made over large ranges of temperature and pressure.展开更多
A detailed fracture mechanics analysis of bridge-toughening in a fiber reinforced composite is presented in this paper. The integral equation governing bridge-toughening as well as crack opening displacement (COD) for...A detailed fracture mechanics analysis of bridge-toughening in a fiber reinforced composite is presented in this paper. The integral equation governing bridge-toughening as well as crack opening displacement (COD) for the composite with interfacial layer is derived from the Castigliano's theorem and interface shear-lag model. A numerical result of the COD equation is obtained using the iteration solution of the second Fredholm integral equation. In order to investigate the effect of various parameters on the toughening, an approximate analytical solution of the equation is present and its error analysis is performed, which demonstrates the approximate solution to be appropriate. A parametric study of the influence of the crack length, interfacial shear modules, thickness of the interphase, fiber radius, fiber volume fraction and properties of materials on composite toughening is therefore carried out. The results are useful for experimental demonstration and toughening design including the fabrication process of the composite.展开更多
According to the boundary condition with the zero,negative,or positive velocity,the initial boundary problem for compressible multi-phase flow with the Dirichlet-type boundary condition can be classified into three ca...According to the boundary condition with the zero,negative,or positive velocity,the initial boundary problem for compressible multi-phase flow with the Dirichlet-type boundary condition can be classified into three cases:impermeable problem,inflow problem,or outflow problem.In this paper,we review the recent progress on the existence and nonlinear stability of the stationary solution to the outflow/inflow problems for viscous multi-phase flow.展开更多
In this paper, the author studies the multidimensional stability of subsonic phase transitions in a steady supersonic flow of van der Waals type. The viscosity capillarity criterion （in ＂Arch. Rat. Mech. Anal., 81（...In this paper, the author studies the multidimensional stability of subsonic phase transitions in a steady supersonic flow of van der Waals type. The viscosity capillarity criterion （in ＂Arch. Rat. Mech. Anal., 81（4）, 1983, 301-315＂） is used to seek physical admissible planar waves. By showing the Lopatinski determinant being non-zero, it is proved that subsonic phase transitions are uniformly stable in the sense of Majda （in ＂Mem. Amer. Math. Soc., 41（275）, 1983, 1-95＂） under both one dimensional and multidimensional perturbations.展开更多
文摘The mathematical physics model of mine methane and coal dust explosion propagation was established in the research,by using continuous phase,combustion,par- ticulate equations of mathematical physics.Based upon the data from mine methane drainage roadway explosion,and mine methane and coal dust explosion propagation ex- perimental studies,the numerical emulator system of mine methane and coal dust explo- sion software was developed by using prevalent flow simulation platform,which can be used to simulate the explosion accidents process effectively.In addition,the system can also be used to determine whether coal dust involved in the explosion,and to simulate accurately the transition from deflagration to detonation in methane explosion,propagation velocity of explosion shock,attenuation pattern,and affected area of explosion.
基金supported by National Natural Science Foundation of China(Grant No.12271468)Shandong Province Natural Science Foundation(Grant Nos.ZR2021ZD03 and ZR2021MA010)supported by National Science Foundation of USA(Grant No.DMS2012490)。
文摘In this paper,an efficient fully-decoupled and fully-discrete numerical scheme with second-order temporal accuracy is developed to solve the incompressible hydrodynamically coupled Cahn-Hilliard model for simulating the two-phase fluid flow system.The scheme is developed by combining the finite element method for spatial discretization and several effective time marching approaches,including the pressure-correction projection method for dealing with fluid equations and the explicit-invariant energy quadratization(explicit-IEQ)approach for dealing with coupled nonlinear terms.The obtained scheme is very efficient since it only needs to solve several decoupled,linear elliptic equations with constant coefficients at each time step.We also strictly prove the solvability and unconditional energy stability of the scheme,and verify the accuracy and stability of the scheme through plenty of numerical examples.
基金the funding support from the National Natural Science Foundation of China(51974013 and 11372033)the Open Research Foundation(NEPU-EOR-2019-003)the initiative funding from the University of Science and Technology Beijing.
文摘Fluid flow at nanoscale is closely related to many areas in nature and technology(e.g.,unconventional hydrocarbon recovery,carbon dioxide geo-storage,underground hydrocarbon storage,fuel cells,ocean desalination,and biomedicine).At nanoscale,interfacial forces dominate over bulk forces,and nonlinear effects are important,which significantly deviate from conventional theory.During the past decades,a series of experiments,theories,and simulations have been performed to investigate fluid flow at nanoscale,which has advanced our fundamental knowledge of this topic.However,a critical review is still lacking,which has seriously limited the basic understanding of this area.Therefore herein,we systematically review experimental,theoretical,and simulation works on single-and multi-phases fluid flow at nanoscale.We also clearly point out the current research gaps and future outlook.These insights will promote the significant development of nonlinear flow physics at nanoscale and will provide crucial guidance on the relevant areas.
文摘To improve the accuracy of the conventional finite-difference method, finitedifference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of any-order derivatives derived from Taylor series expansion. Then, a finite-difference numerical modeling method with any evenorder accuracy is utilized to simulate seismic wave propagation in two-phase anisotropic media. Results indicate that modeling accuracy improves with the increase of difference accuracy order number. It is essential to find the optimal order number, grid size, and time step to balance modeling precision and computational complexity. Four kinds of waves, static mode in the source point, SV wave cusps, reflection and transmission waves are observed in two-phase anisotropic media through modeling.
基金supported by National Natural Science Foundation of China(61273197,61503224)Applied Fundamental Research of Qingdao(14-2-4-19-jch)+2 种基金Huangdao District Science and Technology Project(2014-1-33)China Postdoctoral Science Foundation(2015M582115)"Taishan Scholarship"Construction Engineering
文摘The fundamental equations of multiphase flow that have been established so far fall into two main groups, the multifluid model and the mixture model [1] [2]. Because of the different forms of the equations derived from these two models, many disputes arose [1] [3] [4]. This paper deals mainly with the basic principles for establishing the fundamental equations of multiphase flow, namely the principles of consistency, invariance of material coordinates and material indifference. The results lead to the consistent description of the two models.
基金supported by the National Natural Science Foundations of China under Grant Nos.60972025 and 61271206
文摘The modulation instability （MI） induced by cross-phase modulation （XPM） in dispersion-decreasing fiber （DDF）, whose dispersion decreases along the direction of propagation, is solved and analyzed by the pertur- bation method for the extended nonlinear SchrSdinger equation, considering the higher-order dispersion. The change of the gain spectra with incident power and dispersion decaying factor are also given respec- tively. Due to the fourth-order dispersion, XPM occurs at two gain spectral regions in both the normal and the anomalous dispersion regimes of DDF. The two gain spectral regions in the anomalous dispersion regime are larger than those in the normal dispersion ond region in the anomalous dispersion regime is near regime. Moreover, the gain spectrum of the sec- zero compared with that in the normal dispersion regime, indicating that XPM can be easily produced in the anomalous dispersion regime. The spectral width increases with the increase of the incident optical power and the dispersion decaying factor.
基金supported by the Los Alamos National Laboratory,an affir mative action/equal opportunity employer,operated by Los Alamos National Security,LLC,for the National Nuclear Security Administration of the U.S.Department of Energy under contract DE-AC52-06NA25396
文摘This article describes mathematical models for phase separated mixtures of materials that are in pressure and velocity equilibrium but not necessarily temperature equilibrium. General conditions for constitutive models for such mixtures that exhibit a single mixture sound speed are discussed and specific examples are described.
基金supported by Guangdong Provincial Government of China through the“Computational Science Innovative Research Team”program and the Sun Yat-sen University“Hundred Talents Program”(34000-3181201)and the National Natural Science Foundation of China(No.11101446).
文摘Abstract.In this paper,a novel implementation of immersed interface method combined with Stokes solver on a MAC staggered grid for solving the steady two-fluid Stokes equations with interfaces.The velocity components along the interface are introduced as two augmented variables and the resulting augmented equation is then solved by the GMRES method.The augmented variables and/or the forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity,and are interpolated using cubic splines and are then applied to the fluid through the jump conditions.The Stokes equations are discretized on a staggered Cartesian grid via a second order finite difference method and solved by the conjugate gradient Uzawa-typemethod.The numerical results show that the overall scheme is second order accurate.The major advantages of the present IIM-Stokes solver are the efficiency and flexibility in terms of types of fluid flow and different boundary conditions.The proposed method avoids solution of the pressure Poisson equation,and comparisons are made to show the advantages of time savings by the present method.The generalized two-phase Stokes solver with correction terms has also been applied to incompressible two-phase Navier-Stokes flow.
文摘A century ago the classical physics couldn’t explain many atomic physical phenomena. Now the situation has changed. It’s because within the framework of classical physics with the help of Maxwell’s equations we can derive Schrödinger’s equation, which is the foundation of quantum physics. The equations for energy, momentum, frequency and wavelength of the electromagnetic wave in the atom are derived using the model of atom by analogy with the transmission line. The action constant A0 = (μ0/ε0)1/2s02e2 is a key term in the above mentioned equations. Besides the other well-known constants, the only unknown constant in the last expression is a structural constant of the atom s0. We have found that the value of this constant is 8.277 56 and that it shows up as a link between macroscopic and atomic world. After calculating this constant we get the theory of atoms based on Maxwell’s and Lorentz equations only. This theory does not require knowledge of Planck’s constant h, which is replaced with theoretically derived action constant A0, while the replacement for the fine structure constant α-1 is theoretically derived expression 2s02 = 137.036. So, the structural constant s0 replaces both constants h and α. This paper also defines the stationary states of atoms and shows that the maximal atomic number is equal to Zmax = 137. The presented model of the atoms covers three of the four fundamental interactions, namely the electromagnetic, weak and strong interactions.
文摘In this research article, we investigate the stability of a complex dynamical system involving coupled rigid bodies consisting of three equal masses joined by three rigid rods of equal lengths, hinged at each of their bases. The system is free to oscillate in the vertical plane. We obtained the equation of motion using the generalized coordinates and the Euler-Lagrange equations. We then proceeded to study the stability of the dynamical systems using the Jacobian linearization method and subsequently confirmed our result by phase portrait analysis. Finally, we performed MathCAD simulation of the resulting ordinary differential equations, describing the dynamics of the system and obtained the graphical profiles for each generalized coordinates representing the angles measured with respect to the vertical axis. It is discovered that the coupled rigid pendulum gives rise to irregular oscillations with ever increasing amplitude. Furthermore, the resulting phase portrait analysis depicted spiral sources for each of the oscillating masses showing that the system under investigation is unstable.
文摘The main features are the length of the waveguide in one direction, as well as limitations and localization of the wave beam in other areas. There is described the technique of the solution of tasks on distribution of waves in an infinite cylindrical waveguide with a radial crack. Also numerical results are given in the article. Viscous properties of the material are taken into account by means of an integral operator Voltaire. Research is conducted in the framework of the spatial theory of visco elastic. The technique is based on the separation of spatial variables and formulates the boundary eigenvalue problem that can be solved by the method of orthogonal sweep Godunov. In the given paper we obtain numeric values of the phase velocity depending on of wave numbers. The obtained numerical results are compared with the known data. This work is continuation of article [1]. Statement of the problem and methodology of partial solutions are described in [1]. In this work, we present a complete statement of the problem, methods of solution and discuss the numerical results.
文摘Here we review a new class of mixing rules (hat have extended range of mixtures and conditions that can now be described by equation of state models. One characteristic of these mixing rules is that they simultaneously satisfy the boundary conditions of producing a second virial coefficient that is quadratic in mole fraction, and a free energy of mixing like that of an activity coefficient model at high density, though the mixing rule is itself independent of density. We show that using this mixing rule, various asymmetric, highly nonideal mixtures can be accurately described. One serendipitous result is that the parameters in this mixing rule model are almost independent of temperature, which allows accurate extrapolations of phase behavior to be made over large ranges of temperature and pressure.
基金National Natural Science Foundatjon and China Postdoctoral Scjence Fbundation
文摘A detailed fracture mechanics analysis of bridge-toughening in a fiber reinforced composite is presented in this paper. The integral equation governing bridge-toughening as well as crack opening displacement (COD) for the composite with interfacial layer is derived from the Castigliano's theorem and interface shear-lag model. A numerical result of the COD equation is obtained using the iteration solution of the second Fredholm integral equation. In order to investigate the effect of various parameters on the toughening, an approximate analytical solution of the equation is present and its error analysis is performed, which demonstrates the approximate solution to be appropriate. A parametric study of the influence of the crack length, interfacial shear modules, thickness of the interphase, fiber radius, fiber volume fraction and properties of materials on composite toughening is therefore carried out. The results are useful for experimental demonstration and toughening design including the fabrication process of the composite.
基金supported by the National Natural Science Foundation of China(nos.11931010,11871047)the key research project of Academy for Multidisciplinary Studies,Capital Normal University,and by the Capacity Building for Sci-Tech Innovation-Fundamental Scientific Research Funds(no.007/20530290068).
文摘According to the boundary condition with the zero,negative,or positive velocity,the initial boundary problem for compressible multi-phase flow with the Dirichlet-type boundary condition can be classified into three cases:impermeable problem,inflow problem,or outflow problem.In this paper,we review the recent progress on the existence and nonlinear stability of the stationary solution to the outflow/inflow problems for viscous multi-phase flow.
文摘In this paper, the author studies the multidimensional stability of subsonic phase transitions in a steady supersonic flow of van der Waals type. The viscosity capillarity criterion （in ＂Arch. Rat. Mech. Anal., 81（4）, 1983, 301-315＂） is used to seek physical admissible planar waves. By showing the Lopatinski determinant being non-zero, it is proved that subsonic phase transitions are uniformly stable in the sense of Majda （in ＂Mem. Amer. Math. Soc., 41（275）, 1983, 1-95＂） under both one dimensional and multidimensional perturbations.
