The quark meson coupling model is used to investigate the correlation between thenuclear incompressibility K and the third order derivitive K′ of the nuclear matter saturationcurve,the temperature and entropy depende...The quark meson coupling model is used to investigate the correlation between thenuclear incompressibility K and the third order derivitive K′ of the nuclear matter saturationcurve,the temperature and entropy dependence of the nuclear展开更多
The isoscalar giant monopole resonances（ISGMRs）of hypernucleiAA42Ca,AA（122）Sn,andAA（210）Pb are investigated using a fully self-consistent Skyrme-Hartree-Fock plus random phase approximation method.The Skyrme-typ...The isoscalar giant monopole resonances（ISGMRs）of hypernucleiAA42Ca,AA（122）Sn,andAA（210）Pb are investigated using a fully self-consistent Skyrme-Hartree-Fock plus random phase approximation method.The Skyrme-type forces,SGII,No.5 and SAAl,are adopted to describe the nucleon-nucleon,A hyperon-nucleon and A hyperon-A hyperon（AA）interactions,respectively.For a given hyperon fraction,we find that effects of AA interaction on the properties of infinite symmetric nuclear matter and finite hypernuclei are very small.The ISGMR strengths are shifted to the high energy region when two A are added into normal nuclei.The changes are from two parts,one is due to the mean field calculations,and the other is from the residual interaction associated with A hyperons.The constrained energies are increased by about 0.5-0.7MeV,which consequently enhances the effective incompressibility modulus of hypernuclei.展开更多
It is shown that the criterion of incompressibility applicable to any medium, contradicts to the real meaning of this term. On the basis of expression of speed of sound in inhomogeneous medium and generalized equation...It is shown that the criterion of incompressibility applicable to any medium, contradicts to the real meaning of this term. On the basis of expression of speed of sound in inhomogeneous medium and generalized equation of continuity of mass obtained in papers [1,2] respectively, it is proved that so called internal gravitation waves do not exist in nature. This concept appeared as a result of incorrect interpretation of incompressibility of medium. Correct understanding of criteria of compressibility or incompressibility leads to qualitatively new understanding of homogeneity or heterogeneity of medium, in particular—only strongly inhomogeneous medium can be incompressible while weakly inhomogeneous medium is always compressible. Besides, it is shown that in inhomogeneous media additional terms are added to known hydrodynamic (gas dynamic) correlations applicable to any medium which disappear at transfer to homogeneous model of medium.展开更多
This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practi...This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practical engineering fields,such as in short take-off and vertical landing(STOVL)aircraft.Nowadays many intricate phenomena associated with impinging jet flows remain inadequately elucidated,which limits the ability to optimize aircraft design.Given a boundary condition in the inlet,the impinging jet problem is transformed into a Bernoulli-type free boundary problem according to the stream function.Then the variational method is used to study the corresponding variational problem with one parameter,thereby the wellposedness is established.The main conclusion is as follows.For a 3D axisymmetric finitely long nozzle and an infinitely long vertical wall,given an axial velocity in the inlet of nozzle,there exists a unique smooth incom‑pressible impinging jet flow such that the free boundary initiates smoothly at the endpoint of the nozzle and extends to infinity along the vertical wall at far fields.The key point is to investigate the regularity of the corner where the nozzle and the vertical axis intersect.展开更多
This paper explores Maxwell’s analogy idea between electromagnetic field lines and incompressible fluid, and explains Faraday’s law and Maxwell’s formula for displacement currents by means of fluid dynamics theory:...This paper explores Maxwell’s analogy idea between electromagnetic field lines and incompressible fluid, and explains Faraday’s law and Maxwell’s formula for displacement currents by means of fluid dynamics theory: They show the transport properties of electromagnetic field lines as incompressible fluids, not just effects. Combined of the steady electromagnetic fields, Maxwell’s idea of the analogy between the electromagnetic fields and the incompressible fluids has reached a perfect conclusion. Viewing the electromagnetic field as a vacuum state excited by charges, and extending Maxwell analogy, we consider the gravitowagnetic field as a vacuum state excited by mass. This led to the establishment of the generalized Maxwell equations and the application of this new theory to explain various natural phenomena.展开更多
The diffuse-interface immersed boundary method(IBM)possesses excellent capabilities for simulating flows around complex geometries and moving boundaries.In this method,the flow field is solved on a fixed Cartesian mes...The diffuse-interface immersed boundary method(IBM)possesses excellent capabilities for simulating flows around complex geometries and moving boundaries.In this method,the flow field is solved on a fixed Cartesian mesh,while the solid boundary is discretized into a series of Lagrangian points immersed in the flow field.The boundary condition is implemented by introducing a force term into the momentum equation,and the interaction between the immersed boundary and the fluid domain is achieved via an interpolation process.Over the past decades,the diffuse-interface IBM has gained popularity and spawned many variants,effectively handling a wide range of flow problems from isothermal to thermal flows,from laminar to turbulent flows,and from complex geometries to fluidstructure interaction scenarios.This paper first outlines the basic principles of the diffuse-interface IBM,then highlights recent advancements achieved by the authors’research group,and finally shows the method’s excellent numerical performance and wide applicability through several case studies involving complex moving boundary problems.展开更多
This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution ...This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution using the characteristic and energy methods.Then,under the small assumption of the mass of the particle,we show that the solutions decay at the algebraic time-decay rate.Finally,it is also proved that the above rate is optimal.It should be remarked that if the particle in the coupled system vanishes(i.e.f=O),our works coincide with the classical results by Schonbek[32](J Amer Math Soc,1991,4:423-449),which can be regarded as a generalization from a single fuid model to the two-phase fluid one.展开更多
In this paper,we consider an initial boundary value problem for the nonhomo-geneous heat-conducting magnetohydrodynamic fuids when the viscosityμ,magnetic dif-fusivity v and heat conductivity k depend on the temperat...In this paper,we consider an initial boundary value problem for the nonhomo-geneous heat-conducting magnetohydrodynamic fuids when the viscosityμ,magnetic dif-fusivity v and heat conductivity k depend on the temperature according to μ(0)=°,k(0)=08,v(0)=07,withα,>0,β≥0.We prove the global existence of a unique strong solution provided that ■ is suitably small.In addition,we also get some results of the large-time behavior and exponential decay estimates.展开更多
This study investigates the application of Gurney and flight of fragment equations,typically used to predict metal fragment velocities,in modeling the water jet behavior.Three shotgun cartridge sizes were used as the ...This study investigates the application of Gurney and flight of fragment equations,typically used to predict metal fragment velocities,in modeling the water jet behavior.Three shotgun cartridge sizes were used as the energy source:2.59 g,5.83 g,and 7.13 g.Two configurations were tested:standard(full-barrel water load)and"negative 8"(partial water load).High-speed footage captured water column velocities,and Gurney models,including infinitely tamped and open-faced configurations,combined with the flight of fragment model were used to assess prediction accuracy.Results showed charge strength significantly affects water column velocity,with higher strengths yielding greater stability and velocity retention over distance.The infinitely tamped Gurney model closely predicted experimental velocities,deviating by as little as 1.4%for standard charges and 2.8% for negative 8 charges.Additionally,interesting dynamics such as a 1-2°rise in jet height and the rear overtaking the front was observed.These findings have significant implications for optimizing PAN disruptors and enhancing performance in high-velocity fluid applications and explosive breaching systems.展开更多
In this paper, we show that massive envelopes made of highly compressed normal matter surrounding dark objects (DEOs) can curve the surrounding spacetime and make the systems observationally indistinguishable from the...In this paper, we show that massive envelopes made of highly compressed normal matter surrounding dark objects (DEOs) can curve the surrounding spacetime and make the systems observationally indistinguishable from their massive black hole counterparts. DEOs are new astrophysical objects that are made up of entropy-free incompressible supranuclear dense superfluid (SuSu-matter), embedded in flat spacetimes and invisible to outside observers, practically trapped in false vacua. Based on highly accurate numerical modelling of the internal structures of pulsars and massive neutron stars, and in combination with using a large variety of EOSs, we show that the mass range of DEOs is practically unbounded from above: it spans those of massive neutron stars, stellar and even supermassive black holes: thanks to the universal maximum density of normal matter, , beyond which normal matter converts into SuSu-matter. We apply the scenario to the Crab and Vela pulsars, the massive magnetar PSR J0740 6620, the presumably massive NS formed in GW170817, and the SMBHs in Sgr A* and M87*. Our numerical results also reveal that DEO-Envelope systems not only mimic massive BHs nicely but also indicate that massive DEOs can hide vast amounts of matter capable of turning our universe into a SuSu-matter-dominated one, essentially trapped in false vacua.展开更多
Supermassive DEOs (SMDEOs) are cosmologically evolved objects made of irreducible incompressible supranuclear dense superfluids: The state we consider to govern the matter inside the cores of massive neutron stars. Th...Supermassive DEOs (SMDEOs) are cosmologically evolved objects made of irreducible incompressible supranuclear dense superfluids: The state we consider to govern the matter inside the cores of massive neutron stars. These cores are practically trapped in false vacua, rendering their detection by outside observers impossible. Based on massive parallel computations and theoretical investigations, we show that SMDEOs at the centres of spiral galaxies that are surrounded by massive rotating torii of normal matter may serve as powerful sources for gravitational waves carrying away roughly 1042 erg/s. Due to the extensive cooling by GWs, the SMDEO-Torus systems undergo glitching, through which both rotational and gravitational energies are abruptly ejected into the ambient media, during which the topologies of the embedding spacetimes change from curved into flatter ones, thereby triggering a burst gravitational energy of order 1059 erg. Also, the effects of glitches found to alter the force balance of objects in the Lagrangian-L1 region between the central SMDEO-Torus system and the bulge, enforcing the enclosed objects to develop violent motions, that may explain the origin of the rotational curve irregularities observed in the innermost part of spiral galaxies. Our study shows that the generated GWs at the centres of galaxies, which traverse billions of objects during their outward propagations throughout the entire galaxy, lose energy due to repeatedly squeezing and stretching the objects. Here, we find that these interactions may serve as damping processes that give rise to the formation of collective forces f∝m(r)/r, that point outward, endowing the objects with the observed flat rotation curves. Our approach predicts a correlation between the baryonic mass and the rotation velocities in galaxies, which is in line with the Tully-Fisher relation. The here-presented self-consistent approach explains nicely the observed rotation curves without invoking dark matter or modifying Newtonian gravitation in the low-field approximation.展开更多
This paper is devoted to the study of the shape of the free boundary for a threedimensional axisymmetric incompressible impinging jet.To be more precise,we will show that the free boundary is convex to the fluid,provi...This paper is devoted to the study of the shape of the free boundary for a threedimensional axisymmetric incompressible impinging jet.To be more precise,we will show that the free boundary is convex to the fluid,provided that the uneven ground is concave to the fluid.展开更多
We study the incompressible limit of classical solutions to compressible ideal magneto-hydrodynamics in a domain with a flat boundary.The boundary condition is characteristic and the initial data is general.We first e...We study the incompressible limit of classical solutions to compressible ideal magneto-hydrodynamics in a domain with a flat boundary.The boundary condition is characteristic and the initial data is general.We first establish the uniform existence of classical solutions with respect to the Mach number.Then,we prove that the solutions converge to the solution of the incompressible MHD system.In particular,we obtain a stronger convergence result by using the dispersion of acoustic waves in the half space.展开更多
For solving two-dimensional incompressible flow in the vorticity form by the fourth-order compact finite difference scheme and explicit strong stability preserving temporal discretizations,we show that the simple boun...For solving two-dimensional incompressible flow in the vorticity form by the fourth-order compact finite difference scheme and explicit strong stability preserving temporal discretizations,we show that the simple bound-preserving limiter in Li et al.(SIAM J Numer Anal 56:3308–3345,2018)can enforce the strict bounds of the vorticity,if the velocity field satisfies a discrete divergence free constraint.For reducing oscillations,a modified TVB limiter adapted from Cockburn and Shu(SIAM J Numer Anal 31:607–627,1994)is constructed without affecting the bound-preserving property.This bound-preserving finite difference method can be used for any passive convection equation with a divergence free velocity field.展开更多
Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple the...Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.展开更多
In this paper,we prove that there exists a unique local solution for the Cauchy problem of a system of the incompressible Navier-Stokes-Landau-Lifshitz equations with the Dzyaloshinskii-Moriya interaction and V-flow t...In this paper,we prove that there exists a unique local solution for the Cauchy problem of a system of the incompressible Navier-Stokes-Landau-Lifshitz equations with the Dzyaloshinskii-Moriya interaction and V-flow term inR^(2) and R^(3).Our methods rely upon approximating the system with a perturbed parabolic system and parallel transport.展开更多
Transformer has achieved remarkable results in various fields,including its application in modeling dynamic systems governed by partial differential equations.However,transformer still face challenges in achieving lon...Transformer has achieved remarkable results in various fields,including its application in modeling dynamic systems governed by partial differential equations.However,transformer still face challenges in achieving long-term stable predictions for three-dimensional turbulence.In this paper,we propose an implicit factorized transformer(IFactFormer)model,which enables stable training at greater depths through implicit iteration over factorized attention.IFactFormer is applied to large eddy simulation of three-dimensional homogeneous isotropic turbulence(HIT),and is shown to be more accurate than the FactFormer,Fourier neural operator,and dynamic Smagorinsky model(DSM)in the prediction of the velocity spectra,probability density functions of velocity increments and vorticity,temporal evolutions of velocity and vorticity root-mean-square value and isosurface of the normalized vorticity.IFactFormer can achieve long-term stable predictions of a series of turbulence statistics in HIT.Fur-thermore,IFactFormer showcases superior computational efficiency compared to the conventional DSM in large eddy simulation.展开更多
This paper presents a mass and momentum conservative semi-implicit finite volume(FV)scheme for complex non-hydrostatic free surface flows,interacting with moving solid obstacles.A simplified incompressible Baer-Nunzia...This paper presents a mass and momentum conservative semi-implicit finite volume(FV)scheme for complex non-hydrostatic free surface flows,interacting with moving solid obstacles.A simplified incompressible Baer-Nunziato type model is considered for two-phase flows containing a liquid phase,a solid phase,and the surrounding void.According to the so-called diffuse interface approach,the different phases and consequently the void are described by means of a scalar volume fraction function for each phase.In our numerical scheme,the dynamics of the liquid phase and the motion of the solid are decoupled.The solid is assumed to be a moving rigid body,whose motion is prescribed.Only after the advection of the solid volume fraction,the dynamics of the liquid phase is considered.As usual in semi-implicit schemes,we employ staggered Cartesian control volumes and treat the nonlinear convective terms explicitly,while the pressure terms are treated implicitly.The non-conservative products arising in the transport equation for the solid volume fraction are treated by a path-conservative approach.The resulting semi-implicit FV discretization of the mass and momentum equations leads to a mildly nonlinear system for the pressure which can be efficiently solved with a nested Newton-type technique.The time step size is only limited by the velocities of the two phases contained in the domain,and not by the gravity wave speed nor by the stiff algebraic relaxation source term,which requires an implicit discretization.The resulting semi-implicit algorithm is first validated on a set of classical incompressible Navier-Stokes test problems and later also adds a fixed and moving solid phase.展开更多
In this paper, we use Physics-Informed Neural Networks (PINNs) to solve shape optimization problems. These problems are based on incompressible Navier-Stokes equations and phase-field equations. The phase-field functi...In this paper, we use Physics-Informed Neural Networks (PINNs) to solve shape optimization problems. These problems are based on incompressible Navier-Stokes equations and phase-field equations. The phase-field function is used to describe the state of the fluids, and the optimal shape optimization is obtained by using the shape sensitivity analysis based on the phase-field function. The sharp interface is also presented by a continuous function between zero and one with a large gradient. To avoid the numerical solutions falling into the trivial solution, the hard boundary condition is implemented for our PINNs’ training. Finally, numerical results are given to prove the feasibility and effectiveness of the proposed numerical method.展开更多
Hessian matrices are square matrices consisting of all possible combinations of second partial derivatives of a scalar-valued initial function. As such, Hessian matrices may be treated as elementary matrix systems of ...Hessian matrices are square matrices consisting of all possible combinations of second partial derivatives of a scalar-valued initial function. As such, Hessian matrices may be treated as elementary matrix systems of linear second-order partial differential equations. This paper discusses the Hessian and its applications in optimization, and then proceeds to introduce and derive the notion of the Jaffa Transform, a new linear operator that directly maps a Hessian square matrix space to the initial corresponding scalar field in nth dimensional Euclidean space. The Jaffa Transform is examined, including the properties of the operator, the transform of notable matrices, and the existence of an inverse Jaffa Transform, which is, by definition, the Hessian matrix operator. The Laplace equation is then noted and investigated, particularly, the relation of the Laplace equation to Poisson’s equation, and the theoretical applications and correlations of harmonic functions to Hessian matrices. The paper concludes by introducing and explicating the Jaffa Theorem, a principle that declares the existence of harmonic Jaffa Transforms, which are, essentially, Jaffa Transform solutions to the Laplace partial differential equation.展开更多
基金The project supported in part by the National Natural Science Foundation of China and by the Chinese Academy of Sciences under Contract No.LWTZ-1298
文摘The quark meson coupling model is used to investigate the correlation between thenuclear incompressibility K and the third order derivitive K′ of the nuclear matter saturationcurve,the temperature and entropy dependence of the nuclear
基金Supported by the National Natural Science Foundation of China under Grant Nos 11575060,11775014,11505058 and 11435014
文摘The isoscalar giant monopole resonances（ISGMRs）of hypernucleiAA42Ca,AA（122）Sn,andAA（210）Pb are investigated using a fully self-consistent Skyrme-Hartree-Fock plus random phase approximation method.The Skyrme-type forces,SGII,No.5 and SAAl,are adopted to describe the nucleon-nucleon,A hyperon-nucleon and A hyperon-A hyperon（AA）interactions,respectively.For a given hyperon fraction,we find that effects of AA interaction on the properties of infinite symmetric nuclear matter and finite hypernuclei are very small.The ISGMR strengths are shifted to the high energy region when two A are added into normal nuclei.The changes are from two parts,one is due to the mean field calculations,and the other is from the residual interaction associated with A hyperons.The constrained energies are increased by about 0.5-0.7MeV,which consequently enhances the effective incompressibility modulus of hypernuclei.
文摘It is shown that the criterion of incompressibility applicable to any medium, contradicts to the real meaning of this term. On the basis of expression of speed of sound in inhomogeneous medium and generalized equation of continuity of mass obtained in papers [1,2] respectively, it is proved that so called internal gravitation waves do not exist in nature. This concept appeared as a result of incorrect interpretation of incompressibility of medium. Correct understanding of criteria of compressibility or incompressibility leads to qualitatively new understanding of homogeneity or heterogeneity of medium, in particular—only strongly inhomogeneous medium can be incompressible while weakly inhomogeneous medium is always compressible. Besides, it is shown that in inhomogeneous media additional terms are added to known hydrodynamic (gas dynamic) correlations applicable to any medium which disappear at transfer to homogeneous model of medium.
文摘This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practical engineering fields,such as in short take-off and vertical landing(STOVL)aircraft.Nowadays many intricate phenomena associated with impinging jet flows remain inadequately elucidated,which limits the ability to optimize aircraft design.Given a boundary condition in the inlet,the impinging jet problem is transformed into a Bernoulli-type free boundary problem according to the stream function.Then the variational method is used to study the corresponding variational problem with one parameter,thereby the wellposedness is established.The main conclusion is as follows.For a 3D axisymmetric finitely long nozzle and an infinitely long vertical wall,given an axial velocity in the inlet of nozzle,there exists a unique smooth incom‑pressible impinging jet flow such that the free boundary initiates smoothly at the endpoint of the nozzle and extends to infinity along the vertical wall at far fields.The key point is to investigate the regularity of the corner where the nozzle and the vertical axis intersect.
文摘This paper explores Maxwell’s analogy idea between electromagnetic field lines and incompressible fluid, and explains Faraday’s law and Maxwell’s formula for displacement currents by means of fluid dynamics theory: They show the transport properties of electromagnetic field lines as incompressible fluids, not just effects. Combined of the steady electromagnetic fields, Maxwell’s idea of the analogy between the electromagnetic fields and the incompressible fluids has reached a perfect conclusion. Viewing the electromagnetic field as a vacuum state excited by charges, and extending Maxwell analogy, we consider the gravitowagnetic field as a vacuum state excited by mass. This led to the establishment of the generalized Maxwell equations and the application of this new theory to explain various natural phenomena.
基金partially supported by the National Natural Science Foundation of China(Nos.92271103,12202191)。
文摘The diffuse-interface immersed boundary method(IBM)possesses excellent capabilities for simulating flows around complex geometries and moving boundaries.In this method,the flow field is solved on a fixed Cartesian mesh,while the solid boundary is discretized into a series of Lagrangian points immersed in the flow field.The boundary condition is implemented by introducing a force term into the momentum equation,and the interaction between the immersed boundary and the fluid domain is achieved via an interpolation process.Over the past decades,the diffuse-interface IBM has gained popularity and spawned many variants,effectively handling a wide range of flow problems from isothermal to thermal flows,from laminar to turbulent flows,and from complex geometries to fluidstructure interaction scenarios.This paper first outlines the basic principles of the diffuse-interface IBM,then highlights recent advancements achieved by the authors’research group,and finally shows the method’s excellent numerical performance and wide applicability through several case studies involving complex moving boundary problems.
基金supported by the Anhui Provincial Natural Science Foundation(2408085QA031)the third author's work was supported by the National Natural Science Foundation of China(12001033).
文摘This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution using the characteristic and energy methods.Then,under the small assumption of the mass of the particle,we show that the solutions decay at the algebraic time-decay rate.Finally,it is also proved that the above rate is optimal.It should be remarked that if the particle in the coupled system vanishes(i.e.f=O),our works coincide with the classical results by Schonbek[32](J Amer Math Soc,1991,4:423-449),which can be regarded as a generalization from a single fuid model to the two-phase fluid one.
基金supported by the National Natural Science Foundation of China(No.11931013)the Natural Science Foundation of Guangxi Province(No.2022GXNSFDA035078)the Foundamental Research Funds for the Central Universities,CHD(No.300102122115).
文摘In this paper,we consider an initial boundary value problem for the nonhomo-geneous heat-conducting magnetohydrodynamic fuids when the viscosityμ,magnetic dif-fusivity v and heat conductivity k depend on the temperature according to μ(0)=°,k(0)=08,v(0)=07,withα,>0,β≥0.We prove the global existence of a unique strong solution provided that ■ is suitably small.In addition,we also get some results of the large-time behavior and exponential decay estimates.
基金supported and funded internally through Dr. Catherine Johnson's research funds at Missouri S&T
文摘This study investigates the application of Gurney and flight of fragment equations,typically used to predict metal fragment velocities,in modeling the water jet behavior.Three shotgun cartridge sizes were used as the energy source:2.59 g,5.83 g,and 7.13 g.Two configurations were tested:standard(full-barrel water load)and"negative 8"(partial water load).High-speed footage captured water column velocities,and Gurney models,including infinitely tamped and open-faced configurations,combined with the flight of fragment model were used to assess prediction accuracy.Results showed charge strength significantly affects water column velocity,with higher strengths yielding greater stability and velocity retention over distance.The infinitely tamped Gurney model closely predicted experimental velocities,deviating by as little as 1.4%for standard charges and 2.8% for negative 8 charges.Additionally,interesting dynamics such as a 1-2°rise in jet height and the rear overtaking the front was observed.These findings have significant implications for optimizing PAN disruptors and enhancing performance in high-velocity fluid applications and explosive breaching systems.
文摘In this paper, we show that massive envelopes made of highly compressed normal matter surrounding dark objects (DEOs) can curve the surrounding spacetime and make the systems observationally indistinguishable from their massive black hole counterparts. DEOs are new astrophysical objects that are made up of entropy-free incompressible supranuclear dense superfluid (SuSu-matter), embedded in flat spacetimes and invisible to outside observers, practically trapped in false vacua. Based on highly accurate numerical modelling of the internal structures of pulsars and massive neutron stars, and in combination with using a large variety of EOSs, we show that the mass range of DEOs is practically unbounded from above: it spans those of massive neutron stars, stellar and even supermassive black holes: thanks to the universal maximum density of normal matter, , beyond which normal matter converts into SuSu-matter. We apply the scenario to the Crab and Vela pulsars, the massive magnetar PSR J0740 6620, the presumably massive NS formed in GW170817, and the SMBHs in Sgr A* and M87*. Our numerical results also reveal that DEO-Envelope systems not only mimic massive BHs nicely but also indicate that massive DEOs can hide vast amounts of matter capable of turning our universe into a SuSu-matter-dominated one, essentially trapped in false vacua.
文摘Supermassive DEOs (SMDEOs) are cosmologically evolved objects made of irreducible incompressible supranuclear dense superfluids: The state we consider to govern the matter inside the cores of massive neutron stars. These cores are practically trapped in false vacua, rendering their detection by outside observers impossible. Based on massive parallel computations and theoretical investigations, we show that SMDEOs at the centres of spiral galaxies that are surrounded by massive rotating torii of normal matter may serve as powerful sources for gravitational waves carrying away roughly 1042 erg/s. Due to the extensive cooling by GWs, the SMDEO-Torus systems undergo glitching, through which both rotational and gravitational energies are abruptly ejected into the ambient media, during which the topologies of the embedding spacetimes change from curved into flatter ones, thereby triggering a burst gravitational energy of order 1059 erg. Also, the effects of glitches found to alter the force balance of objects in the Lagrangian-L1 region between the central SMDEO-Torus system and the bulge, enforcing the enclosed objects to develop violent motions, that may explain the origin of the rotational curve irregularities observed in the innermost part of spiral galaxies. Our study shows that the generated GWs at the centres of galaxies, which traverse billions of objects during their outward propagations throughout the entire galaxy, lose energy due to repeatedly squeezing and stretching the objects. Here, we find that these interactions may serve as damping processes that give rise to the formation of collective forces f∝m(r)/r, that point outward, endowing the objects with the observed flat rotation curves. Our approach predicts a correlation between the baryonic mass and the rotation velocities in galaxies, which is in line with the Tully-Fisher relation. The here-presented self-consistent approach explains nicely the observed rotation curves without invoking dark matter or modifying Newtonian gravitation in the low-field approximation.
基金supported in part by the National Natural Science Foundation of China(12101088)the Natural Science Foundation of Sichuan Province(2022NSFSC1858)。
文摘This paper is devoted to the study of the shape of the free boundary for a threedimensional axisymmetric incompressible impinging jet.To be more precise,we will show that the free boundary is convex to the fluid,provided that the uneven ground is concave to the fluid.
文摘We study the incompressible limit of classical solutions to compressible ideal magneto-hydrodynamics in a domain with a flat boundary.The boundary condition is characteristic and the initial data is general.We first establish the uniform existence of classical solutions with respect to the Mach number.Then,we prove that the solutions converge to the solution of the incompressible MHD system.In particular,we obtain a stronger convergence result by using the dispersion of acoustic waves in the half space.
文摘For solving two-dimensional incompressible flow in the vorticity form by the fourth-order compact finite difference scheme and explicit strong stability preserving temporal discretizations,we show that the simple bound-preserving limiter in Li et al.(SIAM J Numer Anal 56:3308–3345,2018)can enforce the strict bounds of the vorticity,if the velocity field satisfies a discrete divergence free constraint.For reducing oscillations,a modified TVB limiter adapted from Cockburn and Shu(SIAM J Numer Anal 31:607–627,1994)is constructed without affecting the bound-preserving property.This bound-preserving finite difference method can be used for any passive convection equation with a divergence free velocity field.
基金supported by the NSFC Grant no.12271492the Natural Science Foundation of Henan Province of China Grant no.222300420550+1 种基金supported by the NSFC Grant no.12271498the National Key R&D Program of China Grant no.2022YFA1005202/2022YFA1005200.
文摘Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.
文摘In this paper,we prove that there exists a unique local solution for the Cauchy problem of a system of the incompressible Navier-Stokes-Landau-Lifshitz equations with the Dzyaloshinskii-Moriya interaction and V-flow term inR^(2) and R^(3).Our methods rely upon approximating the system with a perturbed parabolic system and parallel transport.
基金supported by the National Natural Science Foundation of China(Grant No.12172161)the NSFC Basic Science Center Program(Grant No.11988102)+1 种基金the Shenzhen Science and Technology Program(Grant No.KQTD20180411143441009)supported by Center for Computational Science and Engineering of Southern University of Science and Technology.
文摘Transformer has achieved remarkable results in various fields,including its application in modeling dynamic systems governed by partial differential equations.However,transformer still face challenges in achieving long-term stable predictions for three-dimensional turbulence.In this paper,we propose an implicit factorized transformer(IFactFormer)model,which enables stable training at greater depths through implicit iteration over factorized attention.IFactFormer is applied to large eddy simulation of three-dimensional homogeneous isotropic turbulence(HIT),and is shown to be more accurate than the FactFormer,Fourier neural operator,and dynamic Smagorinsky model(DSM)in the prediction of the velocity spectra,probability density functions of velocity increments and vorticity,temporal evolutions of velocity and vorticity root-mean-square value and isosurface of the normalized vorticity.IFactFormer can achieve long-term stable predictions of a series of turbulence statistics in HIT.Fur-thermore,IFactFormer showcases superior computational efficiency compared to the conventional DSM in large eddy simulation.
基金funded by the Italian Ministry of Education,University and Research(MIUR)in the frame of the Departments of Excellence Initiative 2018-2027 attributed to DICAM of the University of Trento(grant L.232/2016)in the frame of the PRIN 2017 project Innovative numerical methods for evolutionary partial differential equations and applications,the PRIN 2022 project High order structure-preserving semi-implicit schemes for hyperbolic equations.D.is member of INdAM GNCS and was also co-funded by the European Union NextGenerationEU(PNRR,Spoke 7 CN HPC).Views and opinions expressed are however those of the author(s)only and do not necessarily reflect those of the European Union or the European Research Council.Neither the European Union nor the granting authority can be held responsible for them.
文摘This paper presents a mass and momentum conservative semi-implicit finite volume(FV)scheme for complex non-hydrostatic free surface flows,interacting with moving solid obstacles.A simplified incompressible Baer-Nunziato type model is considered for two-phase flows containing a liquid phase,a solid phase,and the surrounding void.According to the so-called diffuse interface approach,the different phases and consequently the void are described by means of a scalar volume fraction function for each phase.In our numerical scheme,the dynamics of the liquid phase and the motion of the solid are decoupled.The solid is assumed to be a moving rigid body,whose motion is prescribed.Only after the advection of the solid volume fraction,the dynamics of the liquid phase is considered.As usual in semi-implicit schemes,we employ staggered Cartesian control volumes and treat the nonlinear convective terms explicitly,while the pressure terms are treated implicitly.The non-conservative products arising in the transport equation for the solid volume fraction are treated by a path-conservative approach.The resulting semi-implicit FV discretization of the mass and momentum equations leads to a mildly nonlinear system for the pressure which can be efficiently solved with a nested Newton-type technique.The time step size is only limited by the velocities of the two phases contained in the domain,and not by the gravity wave speed nor by the stiff algebraic relaxation source term,which requires an implicit discretization.The resulting semi-implicit algorithm is first validated on a set of classical incompressible Navier-Stokes test problems and later also adds a fixed and moving solid phase.
文摘In this paper, we use Physics-Informed Neural Networks (PINNs) to solve shape optimization problems. These problems are based on incompressible Navier-Stokes equations and phase-field equations. The phase-field function is used to describe the state of the fluids, and the optimal shape optimization is obtained by using the shape sensitivity analysis based on the phase-field function. The sharp interface is also presented by a continuous function between zero and one with a large gradient. To avoid the numerical solutions falling into the trivial solution, the hard boundary condition is implemented for our PINNs’ training. Finally, numerical results are given to prove the feasibility and effectiveness of the proposed numerical method.
文摘Hessian matrices are square matrices consisting of all possible combinations of second partial derivatives of a scalar-valued initial function. As such, Hessian matrices may be treated as elementary matrix systems of linear second-order partial differential equations. This paper discusses the Hessian and its applications in optimization, and then proceeds to introduce and derive the notion of the Jaffa Transform, a new linear operator that directly maps a Hessian square matrix space to the initial corresponding scalar field in nth dimensional Euclidean space. The Jaffa Transform is examined, including the properties of the operator, the transform of notable matrices, and the existence of an inverse Jaffa Transform, which is, by definition, the Hessian matrix operator. The Laplace equation is then noted and investigated, particularly, the relation of the Laplace equation to Poisson’s equation, and the theoretical applications and correlations of harmonic functions to Hessian matrices. The paper concludes by introducing and explicating the Jaffa Theorem, a principle that declares the existence of harmonic Jaffa Transforms, which are, essentially, Jaffa Transform solutions to the Laplace partial differential equation.
