The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition a...The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition at the corner point. The former can be solved directly by the equilibrium differential equation and the boundary conditions of four edges of the plate. The latter can be solved by using the superposition principle. Making use of the recommended method, the bending of the plate with all kinds of...展开更多
The failure types in gear systems vary,with typical ones mainly including pitting,cracking,wear,and broken teeth.Different modeling and stiffness calculation methods have been developed for various gear failure types....The failure types in gear systems vary,with typical ones mainly including pitting,cracking,wear,and broken teeth.Different modeling and stiffness calculation methods have been developed for various gear failure types.A unified method for typical gear failure modeling and stiffness calculation is introduced in this study by considering the deviations in the time-varying meshing stiffness(TVMS)of faulty gears resulting from the use of different methods.Specifically,a gear tooth is discretized into a large number of microelements expressed with a matrix,and unified models of typical gear failures are built by adjusting the values of the matrix microelements.The values and positions of the microelements in the tooth failure model matrix have the same physical meaning as the parameter variables in the potential energy method(PEM),so the matrix-based failure model can be perfectly matched with PEM.Afterward,a unified method for TVMS is established.Modeling of healthy and faulty gears with pitting,wear,crack,and broken tooth is performed with the matrix equation,and the corresponding TVMS values are calculated by incorporating the matrix models with PEM.On the basis of the results,the mechanism of typical fault types that affect TVMS is analyzed,and the conclusions are verified through the finite element method.The developed unified method is a promising technique for studying the dynamic response characteristics of gear systems with different failure types because of its superiority in eliminating stiffness deviations.展开更多
The Cahn-Hilliard system was proposed to the first time by Chan and Hilliard in 1958.This model(or system of equations)has intrinsic participation energy and materials sciences and depicts significant characteristics ...The Cahn-Hilliard system was proposed to the first time by Chan and Hilliard in 1958.This model(or system of equations)has intrinsic participation energy and materials sciences and depicts significant characteristics of two phase systems relating to the procedures of phase separation when the temperature is constant.For instance,it can be noticed when a binary alloy(“Aluminum+Zinc”or“Iron+Chromium”)is cooled down adequately.In this case,partially or totally nucleation(nucleation means the appearance of nuclides in the material)is observed:the homogeneous material in the initial state gradually turns into inhomogeneous,giving rise to a very accurate dispersive microstructure.Next,when the time scale is slower the microstructure becomes coarse.In this work,to the first time,the unified method is presented to investigate some physical interpretations for the solutions of the Cahn-Hilliard system when its coefficients varying with time,and to show how phase separation of one or two components and their concentrations occurs dynamically in the system.Finally,2D and 3D plots are introduced to add more comprehensive study which help to understand the physical phenomena of this model.The technique applied in this analysis is powerful and efficient,as evidenced by the computational work and results.This technique can also solve a large number of higher-order evolution equations.展开更多
In this paper,we study the high-order nonlinear Schrodinger equation with periodic initial conditions via the unified transform method extended by Fokas and Lenells.For the high-order nonlinear Schrodinger equation,th...In this paper,we study the high-order nonlinear Schrodinger equation with periodic initial conditions via the unified transform method extended by Fokas and Lenells.For the high-order nonlinear Schrodinger equation,the initial value problem on the circle can be expressed in terms of the solution of a Riemann–Hilbert problem.The related jump matrix can be explicitly expressed based on the initial data alone.Furthermore,we present the explicit solution,which corresponds to a one-gap solution.展开更多
In this paper, a finite element method （FEM）-based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated/unsaturated geomaterial is discussed. A program of FEM named as...In this paper, a finite element method （FEM）-based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated/unsaturated geomaterial is discussed. A program of FEM named as SOFT, adopting unified field equations for thermo-hydro-mechanical-air （THMA） behavior of geomaterial and using finite element-finite difference （FE-FD） scheme for so/l-water-air three-phase coupling problem, is used in the numerical simulation. As an application of the newly proposed numerical method, two engineering problems, one for slope failure in unsaturated model ground and another for in situ heating test related to deep geological repository of high-level radioactive waste （HLRW）, are simulated. The model tests on slope failure in unsaturated Shirasu ground, carried out by Kitamura et al. （2007）, is simulated in the framework of soil-water-air three-phase coupling under the condition of constant temperature. While the in situ heating test reported by Munoz （2006） is simulated in the same framework under the conditions of variable temperature hut constant air pressure.展开更多
The higher-order Kaup-Newell equation is examined by applying the Fokas unified method on the half-line.We demonstrate that the solution can be expressed in relation to the resolution of the Riemann-Hilbert problem.Th...The higher-order Kaup-Newell equation is examined by applying the Fokas unified method on the half-line.We demonstrate that the solution can be expressed in relation to the resolution of the Riemann-Hilbert problem.The jump matrix for this problem is derived from the spectral matrix,which is calculated based on both the initial conditions and the boundary conditions.The jump matrix is explicitly dependent and expressed through the spectral functions,which are derived from the initial and boundary information,respectively.These spectral functions are interdependent and adhere to a so-called global relationship.展开更多
In this paper, the Fokas unified method is used to analyze the initial-boundary value problem of a complex Sharma–Tasso–Olver(c STO) equation on the half line. We show that the solution can be expressed in terms of ...In this paper, the Fokas unified method is used to analyze the initial-boundary value problem of a complex Sharma–Tasso–Olver(c STO) equation on the half line. We show that the solution can be expressed in terms of the solution of a Riemann–Hilbert problem. The relevant jump matrices are explicitly given in terms of the matrix-value spectral functions spectral functions {a(λ), b(λ)} and {A(λ), B(λ)}, which depending on initial data u_0(x) = u(x, 0) and boundary data g_0(y) = u(0, y), g_1(y) = ux(0, y), g_2(y) = u_(xx)(0, y). These spectral functions are not independent, they satisfy a global relation.展开更多
The paper addresses the thermophoretic motion(TM) equation, which is serviced to describe soliton-like thermophoresis of wrinkles in graphene sheet based on Korteweg-de Vries(KdV) equation. The generalized uni?ed meth...The paper addresses the thermophoretic motion(TM) equation, which is serviced to describe soliton-like thermophoresis of wrinkles in graphene sheet based on Korteweg-de Vries(KdV) equation. The generalized uni?ed method is capitalized to construct wrinkle-like multiple soliton solutions. Graphical analysis of one, two, and threesoliton solutions is carried out to depict certain properties like width, amplitude, shape, and open direction are adjustable through various parameters.展开更多
The perturbed nonlinear Schrodinger equation(PNLSE)describes the pulse propagation in optical fibers,which results from the interaction of the higher-order dispersion effect,self-steepening(SS)and self-phase modulatio...The perturbed nonlinear Schrodinger equation(PNLSE)describes the pulse propagation in optical fibers,which results from the interaction of the higher-order dispersion effect,self-steepening(SS)and self-phase modulation(SPM).The challenge between these aforementioned phenomena may lead to a dominant one among them.It is worth noticing that the study of modulation instability(MI)leads to the inspection of dominant phenomena(DPh).Indeed,the MI triggers when the coefficient of DPh exceeds a critical value and it may occur that the interaction leads to wave compression.The PNLSE is currently studied in the literature,mainly on finding traveling wave solutions.Here,we are concerned with analyzing the similarity solutions of the PNLSE.The exact solutions are obtained via introducing similarity transformations and by using the extended unified method.The solutions are evaluated numerically and they are shown graphically.It is observed that the intensity of the pulses exhibits self steepening which progresses to shock soliton in ultrashort time(or near t=0).Also,it is found that the real part of the solution exhibits self-phase modulation in time.The study of(MI)determines the critical value for the coefficients of SS,SPM,or high dispersivity to occur.展开更多
The wave-operator nonlinear Schrödinger equation was introduced in the literature.Further,nonlocal space-time reverse complex field equations were also recently introduced.Studies in this area were focused on emp...The wave-operator nonlinear Schrödinger equation was introduced in the literature.Further,nonlocal space-time reverse complex field equations were also recently introduced.Studies in this area were focused on employing the inverse scattering method and Darboux transformation.Here,we present an approach to find the solutions of the wave-operator nonlinear Schrödinger equation with space and time reverse(W-O-NLSE-STR).It is based on implementing the unified method together with introducing a conventional formulation of the solutions.Indeed,a field and a reverse field may be generated.So,for deriving the solutions of W-O-NLSE-STR,it is evident to distinguish two cases(when the field and its reverse are interactive or not-interactive).In the non-interactive and interactive cases,exact and approximate solutions are obtained.In both cases,the solutions are evaluated numerically and they are displayed graphically.It is observed that the field exhibits solitons propagating essentially(or mainly)on the negative space variable,while those of the reverse field propagate on the other side(or vice versa).These results are completely novel,and we think that it is an essential behavior that characterizes a complex field system with STR.On the other hand,they may exhibit right and left cable patterns(or vice versa).It is found that the solutions of the field and its reverse exhibit self-phase modulation by solitary waves.In the interactive case,the pulses of the field and its reverse propagate in the whole space.The analysis of modulation stability shows that,when the field is stable,its reverse is unstable or both are stable.This holds whenever the polarization of the medium is selfdefocusing.展开更多
In this paper,we apply Fokas unified method to study the initial boundary value(IBV)problems for nonlinear integrable equation with 3×3 Lax pair on the finite interval[0,L].The solution can be expressed by the so...In this paper,we apply Fokas unified method to study the initial boundary value(IBV)problems for nonlinear integrable equation with 3×3 Lax pair on the finite interval[0,L].The solution can be expressed by the solution of a 3×3 Riemann-Hilbert(RH)problem.The relevant jump matrices are written in terms of matrix-value spectral functions s(k),S(k),S_(l)(k),which are determined by initial data at t=0,boundary values at x=0 and boundary values at x=L,respectively.What's more,since the eigenvalues of 3×3 coefficient matrix of k spectral parameter in Lax pair are three different values,search for the path of analytic functions in RH problem becomes a very interesting thing.展开更多
In this paper,we extend the unified gas-kinetic wave-particle(UGKWP)methods to the multi-species gas mixture and multiscale plasma transport.The construction of the scheme is based on the direct modeling on the mesh s...In this paper,we extend the unified gas-kinetic wave-particle(UGKWP)methods to the multi-species gas mixture and multiscale plasma transport.The construction of the scheme is based on the direct modeling on the mesh size and time step scales,and the local cell’s Knudsen number determines the flow physics.The proposed scheme has the multiscale and asymptotic complexity diminishing properties.The multiscale property means that according to the cell’s Knudsen number the scheme can capture the non-equilibrium flow physics when the cell size is on the kinetic mean free path scale,and preserve the asymptotic Euler,Navier-Stokes,and magnetohydrodynamics(MHD)when the cell size is on the hydrodynamic scale and is much larger than the particle mean free path.The asymptotic complexity diminishing property means that the total degrees of freedom of the scheme reduce automatically with the decreasing of the cell’s Knudsen number.In the continuum regime,the scheme automatically degenerates from a kinetic solver to a hydrodynamic solver.In the UGKWP,the evolution of microscopic velocity distribution is coupled with the evolution of macroscopic variables,and the particle evolution as well as the macroscopic fluxes is modeled from a time accumulating solution of kinetic scale particle transport and collision up to a time step scale.For plasma transport,the current scheme provides a smooth transition from particle-in-cell(PIC)method in the rarefied regime to the magnetohydrodynamic solver in the continuum regime.In the continuum limit,the cell size and time step of the UGKWP method are not restricted by the particle mean free path and mean collision time.In the highly magnetized regime,the cell size and time step are not restricted by the Debye length and plasma cyclotron period.The multiscale and asymptotic complexity diminishing properties of the scheme are verified by numerical tests in multiple flow regimes.展开更多
In this work,we present a unified transformation method directly by using the inverse scattering method for a generalized derivative nonlinear Schrödinger(DNLS)equation.By establishing a matrix Riemann-Hilbert pr...In this work,we present a unified transformation method directly by using the inverse scattering method for a generalized derivative nonlinear Schrödinger(DNLS)equation.By establishing a matrix Riemann-Hilbert problem and reconstructing potential function q(x,t)from eigenfunctions{Gj(x,t,η)}3/1 in the inverse problem,the initial-boundary value problems for the generalized DNLS equation on the half-line are discussed.Moreover,we also obtain that the spectral functions f(η),s(η),F(η),S(η)are not independent of each other,but meet an important global relation.As applications,the generalized DNLS equation can be reduced to the Kaup-Newell equation and Chen-Lee-Liu equation on the half-line.展开更多
The existence of high-density bedding planes is a typical characteristic of shale oil reservoirs.Understanding the behavior of hydraulic fracturing in high-density laminated rocks is significant for promoting shale oi...The existence of high-density bedding planes is a typical characteristic of shale oil reservoirs.Understanding the behavior of hydraulic fracturing in high-density laminated rocks is significant for promoting shale oil production.In this study,a hydraulic fracturing model considering tensile failure and frictional slip of the bedding planes is established within the framework of the unified pipe-interface element method(UP-IEM).The model developed for simulating the interaction between the hydraulic fracture and the bedding plane is validated by comparison with experimental results.The hydraulic fracturing patterns in sealed and unsealed bedding planes are compared.Additionally,the effects of differential stress,bedding plane permeability,spacing,and the friction coefficient of the bedding plane are investigated.The results showed that a single main fracture crossing the bedding planes is more likely to form in sealed bedding planes under high differential stress.The decrease in bedding plane permeability and the increase in the friction coefficient also promote the fracture propagating perpendicular to the bedding planes.Shale with high-density bedding planes has a poorer fracturing effect than that with low-density bedding planes,as the hydraulic fracture is prone to initiate and propagate along the bedding planes.Moreover,higher injection pressure is needed to maintain fracture propagation along the bedding.An increase in bedding density will lead to a smaller fracturing area.Fracturing fluid seepage into the bedding planes slows shale fracturing.It is recommended that increasing the injection flow rate,selecting alternative fracturing fluids,and employing multi-well/multi-cluster fracturing may be efficient methods to improve energy production in shale oil reservoirs.展开更多
It is commonly recognized that,despite current analytical approaches,many physical aspects of nonlinear models remain unknown.It is critical to build more efficient integration methods to design and construct numerous...It is commonly recognized that,despite current analytical approaches,many physical aspects of nonlinear models remain unknown.It is critical to build more efficient integration methods to design and construct numerous other unknown solutions and physical attributes for the nonlinear models,as well as for the benefit of the largest audience feasible.To achieve this goal,we propose a new extended unified auxiliary equation technique,a brand-new analytical method for solving nonlinear partial differential equations.The proposed method is applied to the nonlinear Schrödinger equation with a higher dimension in the anomalous dispersion.Many interesting solutions have been obtained.Moreover,to shed more light on the features of the obtained solutions,the figures for some obtained solutions are graphed.The propagation characteristics of the generated solutions are shown.The results show that the proper physical quantities and nonlinear wave qualities are connected to the parameter values.It is worth noting that the new method is very effective and efficient,and it may be applied in the realisation of novel solutions.展开更多
A coupled gas-kinetic scheme(GKS)and unified gas-kinetic wave-particle(UGKWP)method for the disperse dilute gas-particle multiphaseflow is proposed.In the two-phaseflow,the gas phase is always in the hydrodynamic regi...A coupled gas-kinetic scheme(GKS)and unified gas-kinetic wave-particle(UGKWP)method for the disperse dilute gas-particle multiphaseflow is proposed.In the two-phaseflow,the gas phase is always in the hydrodynamic regime and is fol-lowed by GKS for the Navier-Stokes solution.The particle phase is solved by UGKWP in all regimes from particle trajectory crossing to the hydrodynamic wave interac-tion with the variation of particle’s Knudsen number.In the intensive particle colli-sion regime,the UGKWP gives a hydrodynamic wave representation for the particle phase and the GKS-UGKWP for the two-phaseflow reduces to the two-fluid Eulerian-Eulerian(EE)model.In the rarefied regime,the UGKWP tracks individual particle and the GKS-UGKWP goes back to the Eulerian-Lagrangian(EL)formulation.In the tran-sition regime for the solid particle,the GKS-UGKWP takes an optimal choice for the wave and particle decomposition for the solid particle phase and connects the EE and EL methods seamlessly.The GKS-UGKWP method will be tested in allflow regimes with a large variation of Knudsen number for the solid particle transport and Stokes number for the two-phase interaction.It is confirmed that GKS-UGKWP is an efficient and accurate multiscale method for the gas-particle two-phaseflow.展开更多
In this paper,a unified solution method for analyzing the free vibration characteristics of functionally graded rotating type plate(FGRTP)of which the distribution of material is defined by four parameters is presente...In this paper,a unified solution method for analyzing the free vibration characteristics of functionally graded rotating type plate(FGRTP)of which the distribution of material is defined by four parameters is presented.It is assumed that the considered functionally graded materials(FGM)are distributed in the thickness direction according to four parameters.The displacement fields of any point on the FGRTP are determined by the first order shear deformation theory(FSDT),and all displacement functions are extended by ultraspherical polynomial.By applying the Ritz method to the energy function of the whole system,the constitutive equation of FGRTP is obtained and the natural frequencies are obtained by solving the eigenvalue problem.The boundary conditions are generalized to arbitrary boundary conditions by artificial elastic technique.The accuracy of the proposed method is verified by comparing with the previous literatures.The effects of different parameters on the free vibration characteristics of FGRTP are studied through some numerical examples.展开更多
This paper presents a new concept called Unified and Integrated Method for a shear deformable beam element.In this method,Timoshenko beam theory is unified and integrated in such a way that takes into account the effe...This paper presents a new concept called Unified and Integrated Method for a shear deformable beam element.In this method,Timoshenko beam theory is unified and integrated in such a way that takes into account the effect of transverse shear and maintains the shear locking free condition at the same time to generate proper behavior in the analysis of thin to thick beams.The unified and integrated method is applied to finite element analysis(FEA)and isogeometric analysis(IGA)on two-node beam element.This method will be used to analyze uniformly loaded beams with various boundary conditions.A shear influence factor of f,which is a function of beam thickness ratio(L/h),is expressed explicitly as control of the transverse shear strain effect.The analysis gives interesting results showing that applying the unified and integrated method in FEA and IGA will yield exact values of DOF’s and displacement function even when using only a single element.Numerical examples demonstrate the validity and efficiency of the unified and integrated methods.展开更多
Marine structures are mostly made of metals and always experience complex random loading during their service periods. The fatigue crack growth behaviors of metal materials have been proved from laboratory tests to be...Marine structures are mostly made of metals and always experience complex random loading during their service periods. The fatigue crack growth behaviors of metal materials have been proved from laboratory tests to be sensitive to the loading sequence encountered. In order to take account of the loading sequence effect, fatigue life prediction should be based on fatigue crack propagation（FCP） theory rather than the currently used cumulative fatigue damage（CFD） theory. A unified fatigue life prediction（UFLP） method for marine structures has been proposed by the authors＇ group. In order to apply the UFLP method for newly designed structures, authorities such as the classification societies should provide a standardized load-time history（SLH） such as the TWIST and FALSTAFF sequences for transport and fighter aircraft. This paper mainly aims at proposing a procedure to generate the SLHs for marine structures based on a short-term loading sample and to provide an illustration on how to use the presented SLH to a typical tubular T-joint in an offshore platform based on the UFLP method.展开更多
文摘The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition at the corner point. The former can be solved directly by the equilibrium differential equation and the boundary conditions of four edges of the plate. The latter can be solved by using the superposition principle. Making use of the recommended method, the bending of the plate with all kinds of...
基金supported in part by the National Natural Science Foundation of China(Grant Nos.52175122 and 52075456)the Sichuan Science and Technology Program,China(Grant No.2023NSFSC0362)+1 种基金the Sichuan Province Innovative Talent Funding Project for Postdoctoral Fellows,China(Grant No.BX202214)the China Postdoctoral Science Foundation(Grant No.2023M732917).
文摘The failure types in gear systems vary,with typical ones mainly including pitting,cracking,wear,and broken teeth.Different modeling and stiffness calculation methods have been developed for various gear failure types.A unified method for typical gear failure modeling and stiffness calculation is introduced in this study by considering the deviations in the time-varying meshing stiffness(TVMS)of faulty gears resulting from the use of different methods.Specifically,a gear tooth is discretized into a large number of microelements expressed with a matrix,and unified models of typical gear failures are built by adjusting the values of the matrix microelements.The values and positions of the microelements in the tooth failure model matrix have the same physical meaning as the parameter variables in the potential energy method(PEM),so the matrix-based failure model can be perfectly matched with PEM.Afterward,a unified method for TVMS is established.Modeling of healthy and faulty gears with pitting,wear,crack,and broken tooth is performed with the matrix equation,and the corresponding TVMS values are calculated by incorporating the matrix models with PEM.On the basis of the results,the mechanism of typical fault types that affect TVMS is analyzed,and the conclusions are verified through the finite element method.The developed unified method is a promising technique for studying the dynamic response characteristics of gear systems with different failure types because of its superiority in eliminating stiffness deviations.
基金supported by Deanship of Scientific Re-search,Islamic University of Madinah(project Number:442/2020).
文摘The Cahn-Hilliard system was proposed to the first time by Chan and Hilliard in 1958.This model(or system of equations)has intrinsic participation energy and materials sciences and depicts significant characteristics of two phase systems relating to the procedures of phase separation when the temperature is constant.For instance,it can be noticed when a binary alloy(“Aluminum+Zinc”or“Iron+Chromium”)is cooled down adequately.In this case,partially or totally nucleation(nucleation means the appearance of nuclides in the material)is observed:the homogeneous material in the initial state gradually turns into inhomogeneous,giving rise to a very accurate dispersive microstructure.Next,when the time scale is slower the microstructure becomes coarse.In this work,to the first time,the unified method is presented to investigate some physical interpretations for the solutions of the Cahn-Hilliard system when its coefficients varying with time,and to show how phase separation of one or two components and their concentrations occurs dynamically in the system.Finally,2D and 3D plots are introduced to add more comprehensive study which help to understand the physical phenomena of this model.The technique applied in this analysis is powerful and efficient,as evidenced by the computational work and results.This technique can also solve a large number of higher-order evolution equations.
基金funded by National Natural Science Foundation of China(No.11471215)。
文摘In this paper,we study the high-order nonlinear Schrodinger equation with periodic initial conditions via the unified transform method extended by Fokas and Lenells.For the high-order nonlinear Schrodinger equation,the initial value problem on the circle can be expressed in terms of the solution of a Riemann–Hilbert problem.The related jump matrix can be explicitly expressed based on the initial data alone.Furthermore,we present the explicit solution,which corresponds to a one-gap solution.
文摘In this paper, a finite element method （FEM）-based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated/unsaturated geomaterial is discussed. A program of FEM named as SOFT, adopting unified field equations for thermo-hydro-mechanical-air （THMA） behavior of geomaterial and using finite element-finite difference （FE-FD） scheme for so/l-water-air three-phase coupling problem, is used in the numerical simulation. As an application of the newly proposed numerical method, two engineering problems, one for slope failure in unsaturated model ground and another for in situ heating test related to deep geological repository of high-level radioactive waste （HLRW）, are simulated. The model tests on slope failure in unsaturated Shirasu ground, carried out by Kitamura et al. （2007）, is simulated in the framework of soil-water-air three-phase coupling under the condition of constant temperature. While the in situ heating test reported by Munoz （2006） is simulated in the same framework under the conditions of variable temperature hut constant air pressure.
文摘The higher-order Kaup-Newell equation is examined by applying the Fokas unified method on the half-line.We demonstrate that the solution can be expressed in relation to the resolution of the Riemann-Hilbert problem.The jump matrix for this problem is derived from the spectral matrix,which is calculated based on both the initial conditions and the boundary conditions.The jump matrix is explicitly dependent and expressed through the spectral functions,which are derived from the initial and boundary information,respectively.These spectral functions are interdependent and adhere to a so-called global relationship.
基金Supported by National Natural Science Foundation of China under Grant Nos.11271008 and 61072147
文摘In this paper, the Fokas unified method is used to analyze the initial-boundary value problem of a complex Sharma–Tasso–Olver(c STO) equation on the half line. We show that the solution can be expressed in terms of the solution of a Riemann–Hilbert problem. The relevant jump matrices are explicitly given in terms of the matrix-value spectral functions spectral functions {a(λ), b(λ)} and {A(λ), B(λ)}, which depending on initial data u_0(x) = u(x, 0) and boundary data g_0(y) = u(0, y), g_1(y) = ux(0, y), g_2(y) = u_(xx)(0, y). These spectral functions are not independent, they satisfy a global relation.
文摘The paper addresses the thermophoretic motion(TM) equation, which is serviced to describe soliton-like thermophoresis of wrinkles in graphene sheet based on Korteweg-de Vries(KdV) equation. The generalized uni?ed method is capitalized to construct wrinkle-like multiple soliton solutions. Graphical analysis of one, two, and threesoliton solutions is carried out to depict certain properties like width, amplitude, shape, and open direction are adjustable through various parameters.
文摘The perturbed nonlinear Schrodinger equation(PNLSE)describes the pulse propagation in optical fibers,which results from the interaction of the higher-order dispersion effect,self-steepening(SS)and self-phase modulation(SPM).The challenge between these aforementioned phenomena may lead to a dominant one among them.It is worth noticing that the study of modulation instability(MI)leads to the inspection of dominant phenomena(DPh).Indeed,the MI triggers when the coefficient of DPh exceeds a critical value and it may occur that the interaction leads to wave compression.The PNLSE is currently studied in the literature,mainly on finding traveling wave solutions.Here,we are concerned with analyzing the similarity solutions of the PNLSE.The exact solutions are obtained via introducing similarity transformations and by using the extended unified method.The solutions are evaluated numerically and they are shown graphically.It is observed that the intensity of the pulses exhibits self steepening which progresses to shock soliton in ultrashort time(or near t=0).Also,it is found that the real part of the solution exhibits self-phase modulation in time.The study of(MI)determines the critical value for the coefficients of SS,SPM,or high dispersivity to occur.
文摘The wave-operator nonlinear Schrödinger equation was introduced in the literature.Further,nonlocal space-time reverse complex field equations were also recently introduced.Studies in this area were focused on employing the inverse scattering method and Darboux transformation.Here,we present an approach to find the solutions of the wave-operator nonlinear Schrödinger equation with space and time reverse(W-O-NLSE-STR).It is based on implementing the unified method together with introducing a conventional formulation of the solutions.Indeed,a field and a reverse field may be generated.So,for deriving the solutions of W-O-NLSE-STR,it is evident to distinguish two cases(when the field and its reverse are interactive or not-interactive).In the non-interactive and interactive cases,exact and approximate solutions are obtained.In both cases,the solutions are evaluated numerically and they are displayed graphically.It is observed that the field exhibits solitons propagating essentially(or mainly)on the negative space variable,while those of the reverse field propagate on the other side(or vice versa).These results are completely novel,and we think that it is an essential behavior that characterizes a complex field system with STR.On the other hand,they may exhibit right and left cable patterns(or vice versa).It is found that the solutions of the field and its reverse exhibit self-phase modulation by solitary waves.In the interactive case,the pulses of the field and its reverse propagate in the whole space.The analysis of modulation stability shows that,when the field is stable,its reverse is unstable or both are stable.This holds whenever the polarization of the medium is selfdefocusing.
基金supported by the National Natural Science Foundation of China(11901167,11971313 and 51879045)Key scientific research projects of higher education institutions in Henan,China(18B110008).
文摘In this paper,we apply Fokas unified method to study the initial boundary value(IBV)problems for nonlinear integrable equation with 3×3 Lax pair on the finite interval[0,L].The solution can be expressed by the solution of a 3×3 Riemann-Hilbert(RH)problem.The relevant jump matrices are written in terms of matrix-value spectral functions s(k),S(k),S_(l)(k),which are determined by initial data at t=0,boundary values at x=0 and boundary values at x=L,respectively.What's more,since the eigenvalues of 3×3 coefficient matrix of k spectral parameter in Lax pair are three different values,search for the path of analytic functions in RH problem becomes a very interesting thing.
基金supported by National Numerical Windtunnel project and National Science Foundation of China 11772281,91852114.
文摘In this paper,we extend the unified gas-kinetic wave-particle(UGKWP)methods to the multi-species gas mixture and multiscale plasma transport.The construction of the scheme is based on the direct modeling on the mesh size and time step scales,and the local cell’s Knudsen number determines the flow physics.The proposed scheme has the multiscale and asymptotic complexity diminishing properties.The multiscale property means that according to the cell’s Knudsen number the scheme can capture the non-equilibrium flow physics when the cell size is on the kinetic mean free path scale,and preserve the asymptotic Euler,Navier-Stokes,and magnetohydrodynamics(MHD)when the cell size is on the hydrodynamic scale and is much larger than the particle mean free path.The asymptotic complexity diminishing property means that the total degrees of freedom of the scheme reduce automatically with the decreasing of the cell’s Knudsen number.In the continuum regime,the scheme automatically degenerates from a kinetic solver to a hydrodynamic solver.In the UGKWP,the evolution of microscopic velocity distribution is coupled with the evolution of macroscopic variables,and the particle evolution as well as the macroscopic fluxes is modeled from a time accumulating solution of kinetic scale particle transport and collision up to a time step scale.For plasma transport,the current scheme provides a smooth transition from particle-in-cell(PIC)method in the rarefied regime to the magnetohydrodynamic solver in the continuum regime.In the continuum limit,the cell size and time step of the UGKWP method are not restricted by the particle mean free path and mean collision time.In the highly magnetized regime,the cell size and time step are not restricted by the Debye length and plasma cyclotron period.The multiscale and asymptotic complexity diminishing properties of the scheme are verified by numerical tests in multiple flow regimes.
基金supported by the Natural Science Foundation of China(Nos.11601055,11805114 and 11975145)the Natural Science Research Projects of Anhui Province(No.KJ2019A0637)University Excellent Talent Fund of Anhui Province(No.gxyq2019096).
文摘In this work,we present a unified transformation method directly by using the inverse scattering method for a generalized derivative nonlinear Schrödinger(DNLS)equation.By establishing a matrix Riemann-Hilbert problem and reconstructing potential function q(x,t)from eigenfunctions{Gj(x,t,η)}3/1 in the inverse problem,the initial-boundary value problems for the generalized DNLS equation on the half-line are discussed.Moreover,we also obtain that the spectral functions f(η),s(η),F(η),S(η)are not independent of each other,but meet an important global relation.As applications,the generalized DNLS equation can be reduced to the Kaup-Newell equation and Chen-Lee-Liu equation on the half-line.
基金The authors wish to acknowledge the financial support from Key Laboratory of Deep Earth Science and Engineering(Sichuan University),Ministry of Education(DESE202202,H.Y)State Energy Center for Shale Oil Research and Development(33550000-22-ZC0613-0365,H.Y)+2 种基金National Natural Science Foundation of China(42307209,X.Y)China Postdoctoral Science Foundation(2022M712425,X.Y)Shanghai Pujiang Program(2022PJD076,X.Y).
文摘The existence of high-density bedding planes is a typical characteristic of shale oil reservoirs.Understanding the behavior of hydraulic fracturing in high-density laminated rocks is significant for promoting shale oil production.In this study,a hydraulic fracturing model considering tensile failure and frictional slip of the bedding planes is established within the framework of the unified pipe-interface element method(UP-IEM).The model developed for simulating the interaction between the hydraulic fracture and the bedding plane is validated by comparison with experimental results.The hydraulic fracturing patterns in sealed and unsealed bedding planes are compared.Additionally,the effects of differential stress,bedding plane permeability,spacing,and the friction coefficient of the bedding plane are investigated.The results showed that a single main fracture crossing the bedding planes is more likely to form in sealed bedding planes under high differential stress.The decrease in bedding plane permeability and the increase in the friction coefficient also promote the fracture propagating perpendicular to the bedding planes.Shale with high-density bedding planes has a poorer fracturing effect than that with low-density bedding planes,as the hydraulic fracture is prone to initiate and propagate along the bedding planes.Moreover,higher injection pressure is needed to maintain fracture propagation along the bedding.An increase in bedding density will lead to a smaller fracturing area.Fracturing fluid seepage into the bedding planes slows shale fracturing.It is recommended that increasing the injection flow rate,selecting alternative fracturing fluids,and employing multi-well/multi-cluster fracturing may be efficient methods to improve energy production in shale oil reservoirs.
文摘It is commonly recognized that,despite current analytical approaches,many physical aspects of nonlinear models remain unknown.It is critical to build more efficient integration methods to design and construct numerous other unknown solutions and physical attributes for the nonlinear models,as well as for the benefit of the largest audience feasible.To achieve this goal,we propose a new extended unified auxiliary equation technique,a brand-new analytical method for solving nonlinear partial differential equations.The proposed method is applied to the nonlinear Schrödinger equation with a higher dimension in the anomalous dispersion.Many interesting solutions have been obtained.Moreover,to shed more light on the features of the obtained solutions,the figures for some obtained solutions are graphed.The propagation characteristics of the generated solutions are shown.The results show that the proper physical quantities and nonlinear wave qualities are connected to the parameter values.It is worth noting that the new method is very effective and efficient,and it may be applied in the realisation of novel solutions.
基金supported by National Numerical Windtunnel project,National Science Foundation of China(11772281,91852114,12172316)Hong Kong research grant council 16208021Department of Science and Technology of Guangdong Province(Grant No.2020B1212030001).
文摘A coupled gas-kinetic scheme(GKS)and unified gas-kinetic wave-particle(UGKWP)method for the disperse dilute gas-particle multiphaseflow is proposed.In the two-phaseflow,the gas phase is always in the hydrodynamic regime and is fol-lowed by GKS for the Navier-Stokes solution.The particle phase is solved by UGKWP in all regimes from particle trajectory crossing to the hydrodynamic wave interac-tion with the variation of particle’s Knudsen number.In the intensive particle colli-sion regime,the UGKWP gives a hydrodynamic wave representation for the particle phase and the GKS-UGKWP for the two-phaseflow reduces to the two-fluid Eulerian-Eulerian(EE)model.In the rarefied regime,the UGKWP tracks individual particle and the GKS-UGKWP goes back to the Eulerian-Lagrangian(EL)formulation.In the tran-sition regime for the solid particle,the GKS-UGKWP takes an optimal choice for the wave and particle decomposition for the solid particle phase and connects the EE and EL methods seamlessly.The GKS-UGKWP method will be tested in allflow regimes with a large variation of Knudsen number for the solid particle transport and Stokes number for the two-phase interaction.It is confirmed that GKS-UGKWP is an efficient and accurate multiscale method for the gas-particle two-phaseflow.
文摘In this paper,a unified solution method for analyzing the free vibration characteristics of functionally graded rotating type plate(FGRTP)of which the distribution of material is defined by four parameters is presented.It is assumed that the considered functionally graded materials(FGM)are distributed in the thickness direction according to four parameters.The displacement fields of any point on the FGRTP are determined by the first order shear deformation theory(FSDT),and all displacement functions are extended by ultraspherical polynomial.By applying the Ritz method to the energy function of the whole system,the constitutive equation of FGRTP is obtained and the natural frequencies are obtained by solving the eigenvalue problem.The boundary conditions are generalized to arbitrary boundary conditions by artificial elastic technique.The accuracy of the proposed method is verified by comparing with the previous literatures.The effects of different parameters on the free vibration characteristics of FGRTP are studied through some numerical examples.
基金support from the Ministry of Research and Technology/National Research and Inovation Agency(RISTEK-BRIN),Indonesia,through the PDUPT program(Grant No.NKB-1641/UN2.R3.1/HKP.05.00/2019)is gratefully acknowledged.
文摘This paper presents a new concept called Unified and Integrated Method for a shear deformable beam element.In this method,Timoshenko beam theory is unified and integrated in such a way that takes into account the effect of transverse shear and maintains the shear locking free condition at the same time to generate proper behavior in the analysis of thin to thick beams.The unified and integrated method is applied to finite element analysis(FEA)and isogeometric analysis(IGA)on two-node beam element.This method will be used to analyze uniformly loaded beams with various boundary conditions.A shear influence factor of f,which is a function of beam thickness ratio(L/h),is expressed explicitly as control of the transverse shear strain effect.The analysis gives interesting results showing that applying the unified and integrated method in FEA and IGA will yield exact values of DOF’s and displacement function even when using only a single element.Numerical examples demonstrate the validity and efficiency of the unified and integrated methods.
基金financially supported by the Fourth Term of"333 Engineering"Program of Jiangsu Province(Grant No.BRA2011116)Youth Foundation of Jiangsu Province(Grant No.BK2012095)Special Program for Hadal Science and Technology of Shanghai Ocean University(Grant No.HAST-T-2013-01)
文摘Marine structures are mostly made of metals and always experience complex random loading during their service periods. The fatigue crack growth behaviors of metal materials have been proved from laboratory tests to be sensitive to the loading sequence encountered. In order to take account of the loading sequence effect, fatigue life prediction should be based on fatigue crack propagation（FCP） theory rather than the currently used cumulative fatigue damage（CFD） theory. A unified fatigue life prediction（UFLP） method for marine structures has been proposed by the authors＇ group. In order to apply the UFLP method for newly designed structures, authorities such as the classification societies should provide a standardized load-time history（SLH） such as the TWIST and FALSTAFF sequences for transport and fighter aircraft. This paper mainly aims at proposing a procedure to generate the SLHs for marine structures based on a short-term loading sample and to provide an illustration on how to use the presented SLH to a typical tubular T-joint in an offshore platform based on the UFLP method.
