Let(X,φ) be a nonautonomous dynamical system.In this paper,we introduce the notions of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems.Moreover,we establish the v...Let(X,φ) be a nonautonomous dynamical system.In this paper,we introduce the notions of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems.Moreover,we establish the variational principle between the packing topological entropy and the measure-theoretical upper entropy.展开更多
This paper studies the existence of stable standing waves for the nonlinear Schrödinger equation with Hartree-type nonlinearity i∂tψ+Δψ+| ψ |pψ+(| x |−γ∗| ψ |2)ψ=0, (t,x)∈[ 0,T )×ℝN.Where ψ=ψ(t,...This paper studies the existence of stable standing waves for the nonlinear Schrödinger equation with Hartree-type nonlinearity i∂tψ+Δψ+| ψ |pψ+(| x |−γ∗| ψ |2)ψ=0, (t,x)∈[ 0,T )×ℝN.Where ψ=ψ(t,x)is a complex valued function of (t,x)∈ℝ+×ℝN. The parameters N≥3, 0p4Nand 0γmin{ 4,N }. By using the variational methods and concentration compactness principle, we prove the orbital stability of standing waves.展开更多
A three-point fifth-order accurate generalized compact scheme (GC scheme) with a spectral-like resolution is constructed in a general way. The scheme satisfies the principle of stability and the principle about suppre...A three-point fifth-order accurate generalized compact scheme (GC scheme) with a spectral-like resolution is constructed in a general way. The scheme satisfies the principle of stability and the principle about suppression of the oscillations, therefore numerical errors can decay automatically and no spurious oscillations are generated around shocks. The third-order TVD type Runge-Kutta method is employed for the time integration, thus making the GC scheme best suited for unsteady problems. Numerical results show that the GC scheme is shock-capturing. The time-dependent boundary conditions proposed by Thompson are well employed when the algorithm is applied to the Euler equations of gas dynamics.展开更多
There exist two physical constraints upon the motions of celestial systems. Constraint 1 reveals during collapse or explosion motion of celestial bodies that there would be an unattainability upper limit for their com...There exist two physical constraints upon the motions of celestial systems. Constraint 1 reveals during collapse or explosion motion of celestial bodies that there would be an unattainability upper limit for their compact intensity (total mass M/scale size R), which arises from the Lorentz invariance of the time-like metric in local four-dimensional continuum in Einstein’s theory of special relativity. Constraint 2 points that the average mass density of nucleon would be an unsurpassed upper limit for bulk normal matter in nature, which arises from Heisenberg’s uncertainty principle. A very important effect is that the combination of these two physical constraints would prevent the formation of black holes.展开更多
The definition and formula of flexibility of arbitrary rectilinear blocks are introduced and LFF principles are extended to handle arbitrary rectilinear blocks and blocks with relative constraints.The experimental res...The definition and formula of flexibility of arbitrary rectilinear blocks are introduced and LFF principles are extended to handle arbitrary rectilinear blocks and blocks with relative constraints.The experimental results demonstrate the efficiency and effectiveness of the proposed method.展开更多
Micro structures of equal sphere packing （ranging from loose to dense packing） generated numerically by discrete element method under different vibration conditions are characterized using Voronoi/Delaunay tessellat...Micro structures of equal sphere packing （ranging from loose to dense packing） generated numerically by discrete element method under different vibration conditions are characterized using Voronoi/Delaunay tessellation, which is applied on a wide range of packing densities. The analysis on micro properties such as the total perimeter, surface area, and the face number distribution of each Voronoi polyhedron, and the pore size distribution in each Voronoi/Delaunay subunit is systematically carried out. The results show that with the increasing density of sphere packing, the Voronoi//Delaunay pore size distribution is narrowed. That indicates large pores to be gradually substituted by small uniformed ones during densification. Meanwhile, the distributions of face number, total per/meter, and surface area of Voronoi polyhedra at high packing densities tend to be narrower and higher, which is in good agreement with those in random loose packing.展开更多
In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdin...In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L2-concentration and rate of L2-concentration of blow-up solutions.展开更多
In compact spinning with pneumatic groove,the computational fluid dynamic model,computed with parallel technologies & Fluent 6.3,is developed to simulate the flow field in condensing zone with 3D computational flu...In compact spinning with pneumatic groove,the computational fluid dynamic model,computed with parallel technologies & Fluent 6.3,is developed to simulate the flow field in condensing zone with 3D computational fluid dynamic (CFD) technology.Flowing state,distribution rules of static pressure,and velocity in condensing zone are characterized and analyzed.The results show that the fiber bundle in compact spinning with pneumatic groove is compacted by airflow and the shape of the pneumatic groove,and the static pressure in condensing zone is negative,as well as the velocity of airflow in condensing zone is not zero.The fluctuation frequencies of the static pressure and velocity near the bottom of the pneumatic groove are relatively higher,and the number of the fluctuation is equal to that of the round holes in condensing zone.展开更多
Compacting process of fine powder is greatly affected by the aggregate structure of particles. According to the experiment in which several kinds of silicon nitrides in different partical shape and size were compacted...Compacting process of fine powder is greatly affected by the aggregate structure of particles. According to the experiment in which several kinds of silicon nitrides in different partical shape and size were compacted in uniaxialorientation, it is found that the volume compacting rate offorming body differs with the pressure. The aggregatestructure of each sample A, B or C was estimated by applying Cooper's equation to the analysis of the compacting process of each sample展开更多
In this paper,the maximum-principle-preserving(MPP)and positivitypreserving(PP)flux limiting technique will be generalized to a class of high-order weighted compact nonlinear schemes(WCNSs)for scalar conservation laws...In this paper,the maximum-principle-preserving(MPP)and positivitypreserving(PP)flux limiting technique will be generalized to a class of high-order weighted compact nonlinear schemes(WCNSs)for scalar conservation laws and the compressible Euler systems in both one and two dimensions.The main idea of the present method is to rewrite the scheme in a conservative form,and then define the local limiting parameters via case-by-case discussion.Smooth test problems are presented to demonstrate that the proposed MPP/PP WCNSs incorporating a third-order Runge-Kutta method can attain the desired order of accuracy.Other test problems with strong shocks and high pressure and density ratios are also conducted to testify the performance of the schemes.展开更多
We aim at the development of a general modelling workflow for design and optimization of the well flowback and startup operation on hydraulically fractured wells.Fracture flowback model developed earlier by the author...We aim at the development of a general modelling workflow for design and optimization of the well flowback and startup operation on hydraulically fractured wells.Fracture flowback model developed earlier by the authors is extended to take into account several new fluid mechanics factors accompanying flowback,namely,viscoplastic rheology of unbroken cross-linked gel and coupled“fracture-reservoir”numerical submodel for influx from rock formation.We also developed models and implemented new geomechanical factors,namely,(i)fracture closure in gaps between proppant pillars and in proppant-free cavity in the vicinity of the well taking into account formation creep;(ii)propagation of plastic deformations due to tensile rock failure from the fracture face into the fluid-saturated reservoir.We carried out parametric calculations to study the dynamics of fracture conductivity during flowback and its effect on well production for the set of parameters typical of oil wells in Achimov formation of Western Siberia,Russia.The first set of calculations is carried out using the flowback model in the reservoir linear flow regime.It is obtained that the typical length of hydraulic fracture zone,in which tensile rock failure at the fracture walls occurs,is insignificant.In the range of rock permeability in between 0.01 mD and 1 D,we studied the effect of non-dimensional governing parameters as well as bottomhole pressure drop dynamics on oil production.We obtained a map of pressure drop regimes(fast,moderate or slow)leading to maximum cumulative oil production.The second set of parametric calculations is carried out using integrated well production modelling workflow,in which the flowback model acts as a missing link in between hydraulic fracturing and reservoir commercial simulators.We evaluated quantitatively effects of initial fracture aperture,proppant diameter,yield stress of fracturing fluid,pressure drop rate and proppant material type(ceramic and sand)on long-term well production beyond formation linear regime.The third set of parametric calculations is carried out using the flowback model history-matched to field data related to production of four multistage hydraulically fractured oil wells in Achimov formation of Western Siberia,Russia.On the basis of the matched model we evaluated geomechanics effects on fracture conductivity degradation.We also performed sensitivity analysis in the framework of the history-matched model to study the impact of geomechanics and fluid rheology parameters on flowback efficiency.展开更多
基金the National Natural Science Foundation of China (11871188, 12031019)。
文摘Let(X,φ) be a nonautonomous dynamical system.In this paper,we introduce the notions of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems.Moreover,we establish the variational principle between the packing topological entropy and the measure-theoretical upper entropy.
文摘This paper studies the existence of stable standing waves for the nonlinear Schrödinger equation with Hartree-type nonlinearity i∂tψ+Δψ+| ψ |pψ+(| x |−γ∗| ψ |2)ψ=0, (t,x)∈[ 0,T )×ℝN.Where ψ=ψ(t,x)is a complex valued function of (t,x)∈ℝ+×ℝN. The parameters N≥3, 0p4Nand 0γmin{ 4,N }. By using the variational methods and concentration compactness principle, we prove the orbital stability of standing waves.
基金The project supported by the National Natural Science Foundation of China (19972038)Foundation of the National CFD Laboratory of China
文摘A three-point fifth-order accurate generalized compact scheme (GC scheme) with a spectral-like resolution is constructed in a general way. The scheme satisfies the principle of stability and the principle about suppression of the oscillations, therefore numerical errors can decay automatically and no spurious oscillations are generated around shocks. The third-order TVD type Runge-Kutta method is employed for the time integration, thus making the GC scheme best suited for unsteady problems. Numerical results show that the GC scheme is shock-capturing. The time-dependent boundary conditions proposed by Thompson are well employed when the algorithm is applied to the Euler equations of gas dynamics.
文摘There exist two physical constraints upon the motions of celestial systems. Constraint 1 reveals during collapse or explosion motion of celestial bodies that there would be an unattainability upper limit for their compact intensity (total mass M/scale size R), which arises from the Lorentz invariance of the time-like metric in local four-dimensional continuum in Einstein’s theory of special relativity. Constraint 2 points that the average mass density of nucleon would be an unsurpassed upper limit for bulk normal matter in nature, which arises from Heisenberg’s uncertainty principle. A very important effect is that the combination of these two physical constraints would prevent the formation of black holes.
文摘The definition and formula of flexibility of arbitrary rectilinear blocks are introduced and LFF principles are extended to handle arbitrary rectilinear blocks and blocks with relative constraints.The experimental results demonstrate the efficiency and effectiveness of the proposed method.
文摘Micro structures of equal sphere packing （ranging from loose to dense packing） generated numerically by discrete element method under different vibration conditions are characterized using Voronoi/Delaunay tessellation, which is applied on a wide range of packing densities. The analysis on micro properties such as the total perimeter, surface area, and the face number distribution of each Voronoi polyhedron, and the pore size distribution in each Voronoi/Delaunay subunit is systematically carried out. The results show that with the increasing density of sphere packing, the Voronoi//Delaunay pore size distribution is narrowed. That indicates large pores to be gradually substituted by small uniformed ones during densification. Meanwhile, the distributions of face number, total per/meter, and surface area of Voronoi polyhedra at high packing densities tend to be narrower and higher, which is in good agreement with those in random loose packing.
基金supported by National Science Foundation of China (11071177)
文摘In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L2-concentration and rate of L2-concentration of blow-up solutions.
文摘In compact spinning with pneumatic groove,the computational fluid dynamic model,computed with parallel technologies & Fluent 6.3,is developed to simulate the flow field in condensing zone with 3D computational fluid dynamic (CFD) technology.Flowing state,distribution rules of static pressure,and velocity in condensing zone are characterized and analyzed.The results show that the fiber bundle in compact spinning with pneumatic groove is compacted by airflow and the shape of the pneumatic groove,and the static pressure in condensing zone is negative,as well as the velocity of airflow in condensing zone is not zero.The fluctuation frequencies of the static pressure and velocity near the bottom of the pneumatic groove are relatively higher,and the number of the fluctuation is equal to that of the round holes in condensing zone.
文摘Compacting process of fine powder is greatly affected by the aggregate structure of particles. According to the experiment in which several kinds of silicon nitrides in different partical shape and size were compacted in uniaxialorientation, it is found that the volume compacting rate offorming body differs with the pressure. The aggregatestructure of each sample A, B or C was estimated by applying Cooper's equation to the analysis of the compacting process of each sample
基金Project supported by the National Natural Science Foundation of China(No.11571366)the Basic Research Foundation of National Numerical Wind Tunnel Project(No.NNW2018-ZT4A08)
文摘In this paper,the maximum-principle-preserving(MPP)and positivitypreserving(PP)flux limiting technique will be generalized to a class of high-order weighted compact nonlinear schemes(WCNSs)for scalar conservation laws and the compressible Euler systems in both one and two dimensions.The main idea of the present method is to rewrite the scheme in a conservative form,and then define the local limiting parameters via case-by-case discussion.Smooth test problems are presented to demonstrate that the proposed MPP/PP WCNSs incorporating a third-order Runge-Kutta method can attain the desired order of accuracy.Other test problems with strong shocks and high pressure and density ratios are also conducted to testify the performance of the schemes.
文摘We aim at the development of a general modelling workflow for design and optimization of the well flowback and startup operation on hydraulically fractured wells.Fracture flowback model developed earlier by the authors is extended to take into account several new fluid mechanics factors accompanying flowback,namely,viscoplastic rheology of unbroken cross-linked gel and coupled“fracture-reservoir”numerical submodel for influx from rock formation.We also developed models and implemented new geomechanical factors,namely,(i)fracture closure in gaps between proppant pillars and in proppant-free cavity in the vicinity of the well taking into account formation creep;(ii)propagation of plastic deformations due to tensile rock failure from the fracture face into the fluid-saturated reservoir.We carried out parametric calculations to study the dynamics of fracture conductivity during flowback and its effect on well production for the set of parameters typical of oil wells in Achimov formation of Western Siberia,Russia.The first set of calculations is carried out using the flowback model in the reservoir linear flow regime.It is obtained that the typical length of hydraulic fracture zone,in which tensile rock failure at the fracture walls occurs,is insignificant.In the range of rock permeability in between 0.01 mD and 1 D,we studied the effect of non-dimensional governing parameters as well as bottomhole pressure drop dynamics on oil production.We obtained a map of pressure drop regimes(fast,moderate or slow)leading to maximum cumulative oil production.The second set of parametric calculations is carried out using integrated well production modelling workflow,in which the flowback model acts as a missing link in between hydraulic fracturing and reservoir commercial simulators.We evaluated quantitatively effects of initial fracture aperture,proppant diameter,yield stress of fracturing fluid,pressure drop rate and proppant material type(ceramic and sand)on long-term well production beyond formation linear regime.The third set of parametric calculations is carried out using the flowback model history-matched to field data related to production of four multistage hydraulically fractured oil wells in Achimov formation of Western Siberia,Russia.On the basis of the matched model we evaluated geomechanics effects on fracture conductivity degradation.We also performed sensitivity analysis in the framework of the history-matched model to study the impact of geomechanics and fluid rheology parameters on flowback efficiency.
