In the present study,we investigated the existence of arbitrary amplitude dust acoustic solitons by considering the Cairns distributed ions,negatively charged streaming dust grains along with(r,q)distributed electrons...In the present study,we investigated the existence of arbitrary amplitude dust acoustic solitons by considering the Cairns distributed ions,negatively charged streaming dust grains along with(r,q)distributed electrons in an un-magnetized dusty plasma.We used the pseudopotential technique to obtain the solitary wave solution.It is seen that the coexistence of rarefactive and compressive solitons is possible when ions and electrons are nonthermally distributed.We found that the soliton characteristics are strongly dependent on the choice of velocity distribution function through the nonthermal spectral indices r q,,a as well as on the ion and dust temperatures.For(r,q)distributed electrons,we found that the soliton amplitude increases(decreases)with smaller(higher)values of negative(positive)r.For Cairns distributed ions,we found a transition from negative to positive polarity solitary structures with the coexistence in between as the nonthermal parameter a increases.Our results gave a better explanation for the formation of dust acoustic solitary structures and their dependence on high and low energy particles in nonthermal distribution profiles in space environments.展开更多
The governing equation of the dust fluid with non-thermal ions and variable dust charge on dust particles in hot dust plasmas is obtained. Both the compressive and rarefactive waves in this system are investigated. Th...The governing equation of the dust fluid with non-thermal ions and variable dust charge on dust particles in hot dust plasmas is obtained. Both the compressive and rarefactive waves in this system are investigated. They can be determined by plasma parameters including the temperatures of （lust fluid, ions and electrons, as well as the non-thermal parameter of ions, and the number densities of the dust particles, the ions and the electrons, etc.展开更多
Hydrodynamic instability growth at the deuterium-tritium(DT)fuel-ablator interface plays a critical role in determining the performance of inertial confinement fusion implosions.During the late stages of implosion,ins...Hydrodynamic instability growth at the deuterium-tritium(DT)fuel-ablator interface plays a critical role in determining the performance of inertial confinement fusion implosions.During the late stages of implosion,insufficient doping of the ablator material can result in highenergy X-ray preheat,which may trigger the development of a classical-like Rayleigh-Taylor instability(RTI)at the fuel-ablator interface.In implosion experiments at the Shenguang 100 kJ-level laser facility,the primary source of perturbation is the roughness of the inner DT ice interface.In this study,we propose an analytical model to describe the feed-out process of the initial roughness of the inner DT ice interface.The perturbation amplitude derived from this model serves as the initial seed for the late-time RTI during the acceleration phase.Our findings confirm the presence of classical-like RTI at the fuel-ablator interface.Numerical simulations conducted using a radiation hydrodynamic code validate the proposed analytical model and demonstrate the existence of a peak mode number in both the feed-out process and the classical-like RTI.It provides an alternative bridge between the current target fabrication limitations and the unexpected implosion performance.展开更多
The double casing warhead with sandwiched charge is a novel fragmentation warhead that can produce two groups of fragments with different velocity,and the previous work has presented a calculation formula to determine...The double casing warhead with sandwiched charge is a novel fragmentation warhead that can produce two groups of fragments with different velocity,and the previous work has presented a calculation formula to determine the maximum fragment velocity.The current work builds on the published formula to further develop a formula for calculating the axial distribution characteristics of the fragment velocity.For this type of warhead,the simulation of the dispersion characteristics of the detonation products at different positions shows that the detonation products at the ends have a much larger axial velocity than those in the middle,and the detonation products have a greater axial dispersion velocity when they are closer to the central axis.The loading process and the fragment velocity vary with the axial position for both casing layers,and the total velocity of the fragments is the vector sum of the radial velocity and the axial velocity.At the same axial position,the acceleration time of the inner casing is greater than that of the outer casing.For the same casing,the fragments generated at the ends have a longer acceleration time than the fragments from the middle.The proposed formula is validated with the X-ray radiography results of the four warheads previously tested experimentally and the 3D smoothedparticle hydrodynamics numerical simulation results of several series of new warheads with different configurations.The formula can accurately and reliably calculate the fragment velocity when the lengthto-diameter ratio of the charge is greater than 1.5 and the thickness of the casing is less than 20%its inner radius.This work thus provides a key reference for the theoretical analysis and the design of warheads with multiple casings.展开更多
This paper is concerned with the global well-posedness of the solution to the compressible Navier-Stokes/Allen-Cahn system and its sharp interface limit in one-dimensional space.For the perturbations with small energy...This paper is concerned with the global well-posedness of the solution to the compressible Navier-Stokes/Allen-Cahn system and its sharp interface limit in one-dimensional space.For the perturbations with small energy but possibly large oscillations of rarefaction wave solutions near phase separation,and where the strength of the initial phase field could be arbitrarily large,we prove that the solution of the Cauchy problem exists for all time,and converges to the centered rarefaction wave solution of the corresponding standard two-phase Euler equation as the viscosity and the thickness of the interface tend to zero.The proof is mainly based on a scaling argument and a basic energy method.展开更多
Compared with PELE with inert fillings such as polyethylene and nylon,reactive PELE(RPELE)shows excellent damage effects when impacting concrete targets due to the filling deflagration reaction.In present work,an anal...Compared with PELE with inert fillings such as polyethylene and nylon,reactive PELE(RPELE)shows excellent damage effects when impacting concrete targets due to the filling deflagration reaction.In present work,an analytical model describing the jacket deformation and concrete target damage impacted by RPELE was presented,in which the radial rarefaction and filling deflagration reaction were considered.The impact tests of RPELE on concrete target in the 592-1012 m/s were carried out to verify the analytical model.Based on the analytical model,the angle-length evolution mechanism of the jacket bending-curling deformation was revealed,and the concrete target damage was further analyzed.One can find out that the average prediction errors of the front crater,opening and back crater are 6.8%,8.5%and 7.1%,respectively.Moreover,the effects of radial rarefaction and deflagration were discussed.It was found that the neglect of radial rarefaction overestimates the jacket deformation and concrete target damage,while the deflagration reaction of filling increases the diameter of the front crater,opening and back crater by 25.4%,24.3%and 31.1%,respectively.The research provides a valuable reference for understanding and predicting the jacket deformation and concrete target damage impacted by RPELE.展开更多
One of the greatest challenges in the design of a gun is to balance muzzle velocity and recoil,especially for guns on aircrafts and deployable vehicles.To resolve the conflict between gun power and recoil force,a conc...One of the greatest challenges in the design of a gun is to balance muzzle velocity and recoil,especially for guns on aircrafts and deployable vehicles.To resolve the conflict between gun power and recoil force,a concept of rarefaction wave gun(RAVEN)was proposed to significantly reduce the weapon recoil and the heat in barrel,while minimally reducing the muzzle velocity.The main principle of RAVEN is that the rarefaction wave will not reach the projectile base until the muzzle by delaying the venting time of an expansion nozzle at the breech.Developed on the RAVEN principle,the purpose of this paper is to provide an engineering method for predicting the performance of a low-recoil gun with front nozzle.First,a two-dimensional two-phase flow model of interior ballistic during the RAVEN firing cycle was established.Numerical simulation results were compared with the published data to validate the reliability and accuracy.Next,the effects of the vent opening times and locations were investigated to determine the influence rules on the performance of the RAVEN with front nozzle.Then according to the results above,simple nonlinear fitting formulas were provided to explain how the muzzle velocity and the recoil force change with the vent opening time and location.Finally,a better vent venting opening time corresponding to the vent location was proposed.The findings should make an important contribution to the field of engineering applications of the RAVEN.展开更多
This paper is concerned with the stability of the rarefaction wave for the generalized KdV-Burgers equation [GRAPHICS] Roughly speaking, under the assumption that u(-) < u(+), the solution u(x, t) to Cauchy problem...This paper is concerned with the stability of the rarefaction wave for the generalized KdV-Burgers equation [GRAPHICS] Roughly speaking, under the assumption that u(-) < u(+), the solution u(x, t) to Cauchy problem (1) satisfying (sup)(x&ISIN;R)\u(x, t) - u(R)(x/t)\ --> 0 as t --> infinity, where u(R)(x/t) is the rarefaction wave of the non-viscous Burgers equation u(t) + f(u)(x) = 0 with Riemann initial data [GRAPHICS]展开更多
The prediction of the multiscale flow in the Knudsen pump is important for understanding its pumping mechanism.However,there is little research on such interesting multiscale phenomenon in the Knudsen pumps.In this pa...The prediction of the multiscale flow in the Knudsen pump is important for understanding its pumping mechanism.However,there is little research on such interesting multiscale phenomenon in the Knudsen pumps.In this paper,a novel numerical analysis method combining the direct simulation Monte Carlo（DSMC） method with the smoothed particle hydrodynamics（SPH） method is presented for simulating the multiscale flow,which is often encountered in the application of the Knudsen pumps.Validity and accuracy of the new method are given by comparing its results with that of the previous research.Using the coupled multiscale approach,the rarefaction and the temperature drive are studied,which are two main factors on the performance of the Knudsen pumps.To investigate the effect of rarefaction on the performance of the Knudsen pump,various pump operation pressures are compared.The flow characteristics and pumping ability at different rarefaction are analyzed,and the phenomenon of the multiscale flow is also discussed.Several cases with different linear or nonlinear temperature gradients are set to investigate the effect of temperature gradient on the performance of the Knudsen pump.The flow characteristics of the Knudsen pump such as the velocity,pressure increase,and the mass flowrate are presented.A unique phenomenon,the reverse transpiration effect caused by the nonlinear temperature gradient is studied,and the reason of the significant pressure increase in the pump channel is also analyzed.Since the multiscale gas flow is widely encountered in the microflow systems,the above method and its results can also be greatly beneficial and provide significant insights for the design of the MEMS devices.展开更多
Given the definition of the reference Knudsen number for micro gas journal bearings,the range in the number is related to the viscosity of air at different temperatures. A modified Reynolds equation for micro gas jour...Given the definition of the reference Knudsen number for micro gas journal bearings,the range in the number is related to the viscosity of air at different temperatures. A modified Reynolds equation for micro gas journal bearings based on Burgdorfer's first-order slip boundary condition is proposed that takes into account the gas rarefaction effect. The finite difference method (FDM) is adopted to solve the modified Reynolds equation to obtain the pressure profiles,load capacities and attitude angles for micro gas journal bearings at different reference Knudsen numbers,bearing numbers and journal eccentricity ratios. Numerical analysis shows that pressure profiles and non-dimensional load capacities decrease markedly as gas rarefaction in-creases. Attitude angles change conversely,and when the eccentricity ratio is less than 0.6,the attitude angles rise slightly and the influence of the reference Knudsen number is not marked. In addition,the effect of gas rarefaction on the non-dimensional load capacity and attitude angle decreases with smaller bearing numbers.展开更多
Shock wave is emitted into the plate and sphere when a sphere hypervelocity impacts onto a thin plate.The fragmentation and phase change of the material caused by the propagation and unloading of shock wave could resu...Shock wave is emitted into the plate and sphere when a sphere hypervelocity impacts onto a thin plate.The fragmentation and phase change of the material caused by the propagation and unloading of shock wave could result in the formation of debris cloud eventually.Propagation models are deduced based on one-dimensional shock wave theory and the geometry of sphere,which uses elliptic equations(corresponding to ellipsoid equations in physical space)to describe the propagation of shock wave and the rarefaction wave.The“Effective thickness”is defined as the critical plate thickness that ensures the rarefaction wave overtake the shock wave at the back of the sphere.The“Effective thickness”is directly related to the form of the debris cloud.The relation of the“Effective thickness”and the“Optimum thickness”is also discussed.The impacts of Al spheres onto Al plates are simulated within SPH to verify the propagation models and associated theories.The results show that the wave fronts predicted by the propagation models are closer to the simulation result at higher impact velocity.The curvatures of the wave fronts decrease with the increase of impact velocities.The predicted“Effective thickness”is consistent with the simulation results.The analysis about the shock wave propagation and unloading in this paper can provide a new sight and inspiration for the quantitative study of hypervelocity impact and space debris protection.展开更多
In this article, we get non-selfsimilar elementary waves of the conservation laws in another kind of view, which is different from the usual self-similar transformation. The solution has different global structure. Th...In this article, we get non-selfsimilar elementary waves of the conservation laws in another kind of view, which is different from the usual self-similar transformation. The solution has different global structure. This article is divided into three parts. The first part is introduction. In the second part, we discuss non-selfsimilar elementary waves and their interactions of a class of twodimensional conservation laws. In this case, we consider the case that the initial discontinuity is parabola with u＋ 〉 0, while explicit non-selfsirnilar rarefaction wave can be obtained. In the second part, we consider the solution structure of case u＋ 〈 0. The new solution structures are obtained by the interactions between different elementary waves, and will continue to interact with other states. Global solutions would be very different from the situation of one dimension.展开更多
This paper is concerned with the stability of the rarefaction wave for the Burgers equationwhere 0 ≤ a < 1/4p (q is determined by (2.2)). Roughly speaking, under the assumption that u_ < u+, the authors prove t...This paper is concerned with the stability of the rarefaction wave for the Burgers equationwhere 0 ≤ a < 1/4p (q is determined by (2.2)). Roughly speaking, under the assumption that u_ < u+, the authors prove the existence of the global smooth solution to the Cauchy problem (I), also find the solution u(x, t) to the Cauchy problem (I) satisfying sup |u(x, t) -uR(x/t)| → 0 as t → ∞, where uR(x/t) is the rarefaction wave of the non-viscous Burgersequation ut + f(u)x = 0 with Riemann initial data u(x, 0) =展开更多
In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four s...In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections： 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.展开更多
In this article, authors study the Cauch problem for a model of hyperbolic-elliptic coupled system derived from the one-dimensional system of the rudiating gas. By considering the initial data as a small disturbances ...In this article, authors study the Cauch problem for a model of hyperbolic-elliptic coupled system derived from the one-dimensional system of the rudiating gas. By considering the initial data as a small disturbances of rarefaction wave of inviscid Burgers equation, the global existence of the solution to the corresponding Cauchy problem and asymptotic stability of rarefaction wave is proved. The analysis is based on a priori estimates and L^2-energy method.展开更多
In this paper, the Riemann solutions for scalar conservation laws with discontinuous flux function were constructed. The interactions of elementary waves of the conservation laws were concerned, and the numerical simu...In this paper, the Riemann solutions for scalar conservation laws with discontinuous flux function were constructed. The interactions of elementary waves of the conservation laws were concerned, and the numerical simulations were given.展开更多
In this article, we investigate the global stability of the wave patterns with the superposition of viscous contact wave and rarefaction wave for the one-dimensional compressible Navier-Stokes equations with a free bo...In this article, we investigate the global stability of the wave patterns with the superposition of viscous contact wave and rarefaction wave for the one-dimensional compressible Navier-Stokes equations with a free boundary. It is shown that for the ideal polytropic gas, the superposition of the viscous contact wave with rarefaction wave is nonlinearly stable for the free boundary problem under the large initial perturbations for any γ 〉 1 with V being the adiabatic exponent provided that the wave strength is suitably small.展开更多
文摘In the present study,we investigated the existence of arbitrary amplitude dust acoustic solitons by considering the Cairns distributed ions,negatively charged streaming dust grains along with(r,q)distributed electrons in an un-magnetized dusty plasma.We used the pseudopotential technique to obtain the solitary wave solution.It is seen that the coexistence of rarefactive and compressive solitons is possible when ions and electrons are nonthermally distributed.We found that the soliton characteristics are strongly dependent on the choice of velocity distribution function through the nonthermal spectral indices r q,,a as well as on the ion and dust temperatures.For(r,q)distributed electrons,we found that the soliton amplitude increases(decreases)with smaller(higher)values of negative(positive)r.For Cairns distributed ions,we found a transition from negative to positive polarity solitary structures with the coexistence in between as the nonthermal parameter a increases.Our results gave a better explanation for the formation of dust acoustic solitary structures and their dependence on high and low energy particles in nonthermal distribution profiles in space environments.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10575082 and 10247008, the Natural Science Foundation of Gansu Province under Grant No. YS021-A22-018, the Scientific Research Foundation for the Returned 0verseas Chinese Scholars of the Ministry of Education, the Natural Science Foundation of Northwest Normal University under Grant No. NWNU-KJCXGC215, and partially supported by the Foundation of Royal Society K.C. Wong Fellowship of UK
文摘The governing equation of the dust fluid with non-thermal ions and variable dust charge on dust particles in hot dust plasmas is obtained. Both the compressive and rarefactive waves in this system are investigated. They can be determined by plasma parameters including the temperatures of （lust fluid, ions and electrons, as well as the non-thermal parameter of ions, and the number densities of the dust particles, the ions and the electrons, etc.
基金funded by the National Key R&D Program of China(Grant No.2023YFA1608400)the National Natural Science Foundation of China(Grant No.12302281).
文摘Hydrodynamic instability growth at the deuterium-tritium(DT)fuel-ablator interface plays a critical role in determining the performance of inertial confinement fusion implosions.During the late stages of implosion,insufficient doping of the ablator material can result in highenergy X-ray preheat,which may trigger the development of a classical-like Rayleigh-Taylor instability(RTI)at the fuel-ablator interface.In implosion experiments at the Shenguang 100 kJ-level laser facility,the primary source of perturbation is the roughness of the inner DT ice interface.In this study,we propose an analytical model to describe the feed-out process of the initial roughness of the inner DT ice interface.The perturbation amplitude derived from this model serves as the initial seed for the late-time RTI during the acceleration phase.Our findings confirm the presence of classical-like RTI at the fuel-ablator interface.Numerical simulations conducted using a radiation hydrodynamic code validate the proposed analytical model and demonstrate the existence of a peak mode number in both the feed-out process and the classical-like RTI.It provides an alternative bridge between the current target fabrication limitations and the unexpected implosion performance.
基金supported by the National Natural Science Foundation of China(Grant No.11872121)。
文摘The double casing warhead with sandwiched charge is a novel fragmentation warhead that can produce two groups of fragments with different velocity,and the previous work has presented a calculation formula to determine the maximum fragment velocity.The current work builds on the published formula to further develop a formula for calculating the axial distribution characteristics of the fragment velocity.For this type of warhead,the simulation of the dispersion characteristics of the detonation products at different positions shows that the detonation products at the ends have a much larger axial velocity than those in the middle,and the detonation products have a greater axial dispersion velocity when they are closer to the central axis.The loading process and the fragment velocity vary with the axial position for both casing layers,and the total velocity of the fragments is the vector sum of the radial velocity and the axial velocity.At the same axial position,the acceleration time of the inner casing is greater than that of the outer casing.For the same casing,the fragments generated at the ends have a longer acceleration time than the fragments from the middle.The proposed formula is validated with the X-ray radiography results of the four warheads previously tested experimentally and the 3D smoothedparticle hydrodynamics numerical simulation results of several series of new warheads with different configurations.The formula can accurately and reliably calculate the fragment velocity when the lengthto-diameter ratio of the charge is greater than 1.5 and the thickness of the casing is less than 20%its inner radius.This work thus provides a key reference for the theoretical analysis and the design of warheads with multiple casings.
基金supported by the National Natural Science Foundation of China(12361044)supported by the National Natural Science Foundation of China(12171024,11971217,11971020)supported by the Academic and Technical Leaders Training Plan of Jiangxi Province(20212BCJ23027)。
文摘This paper is concerned with the global well-posedness of the solution to the compressible Navier-Stokes/Allen-Cahn system and its sharp interface limit in one-dimensional space.For the perturbations with small energy but possibly large oscillations of rarefaction wave solutions near phase separation,and where the strength of the initial phase field could be arbitrarily large,we prove that the solution of the Cauchy problem exists for all time,and converges to the centered rarefaction wave solution of the corresponding standard two-phase Euler equation as the viscosity and the thickness of the interface tend to zero.The proof is mainly based on a scaling argument and a basic energy method.
基金funding from the National Natural Science Foundation of China(Grant Nos.12132003 and 12302460)。
文摘Compared with PELE with inert fillings such as polyethylene and nylon,reactive PELE(RPELE)shows excellent damage effects when impacting concrete targets due to the filling deflagration reaction.In present work,an analytical model describing the jacket deformation and concrete target damage impacted by RPELE was presented,in which the radial rarefaction and filling deflagration reaction were considered.The impact tests of RPELE on concrete target in the 592-1012 m/s were carried out to verify the analytical model.Based on the analytical model,the angle-length evolution mechanism of the jacket bending-curling deformation was revealed,and the concrete target damage was further analyzed.One can find out that the average prediction errors of the front crater,opening and back crater are 6.8%,8.5%and 7.1%,respectively.Moreover,the effects of radial rarefaction and deflagration were discussed.It was found that the neglect of radial rarefaction overestimates the jacket deformation and concrete target damage,while the deflagration reaction of filling increases the diameter of the front crater,opening and back crater by 25.4%,24.3%and 31.1%,respectively.The research provides a valuable reference for understanding and predicting the jacket deformation and concrete target damage impacted by RPELE.
基金supported by the National Natural Science Foundation of China(Grant No.11502114)the Fundamental Research Funds for the Central Universities(Grant No.30918011323)
文摘One of the greatest challenges in the design of a gun is to balance muzzle velocity and recoil,especially for guns on aircrafts and deployable vehicles.To resolve the conflict between gun power and recoil force,a concept of rarefaction wave gun(RAVEN)was proposed to significantly reduce the weapon recoil and the heat in barrel,while minimally reducing the muzzle velocity.The main principle of RAVEN is that the rarefaction wave will not reach the projectile base until the muzzle by delaying the venting time of an expansion nozzle at the breech.Developed on the RAVEN principle,the purpose of this paper is to provide an engineering method for predicting the performance of a low-recoil gun with front nozzle.First,a two-dimensional two-phase flow model of interior ballistic during the RAVEN firing cycle was established.Numerical simulation results were compared with the published data to validate the reliability and accuracy.Next,the effects of the vent opening times and locations were investigated to determine the influence rules on the performance of the RAVEN with front nozzle.Then according to the results above,simple nonlinear fitting formulas were provided to explain how the muzzle velocity and the recoil force change with the vent opening time and location.Finally,a better vent venting opening time corresponding to the vent location was proposed.The findings should make an important contribution to the field of engineering applications of the RAVEN.
文摘This paper is concerned with the stability of the rarefaction wave for the generalized KdV-Burgers equation [GRAPHICS] Roughly speaking, under the assumption that u(-) < u(+), the solution u(x, t) to Cauchy problem (1) satisfying (sup)(x&ISIN;R)\u(x, t) - u(R)(x/t)\ --> 0 as t --> infinity, where u(R)(x/t) is the rarefaction wave of the non-viscous Burgers equation u(t) + f(u)(x) = 0 with Riemann initial data [GRAPHICS]
基金supported by National Hi-tech Research and Development Program of China (863 Program,Grant Nos.2009AA05Z118,2009AA044801)National Natural Science Foundation of China (Grant Nos. 50475100,51106137)+2 种基金China Postdoctoral Science Foundation (Grant No. 2010047172)Zhejiang Provincial Natural Science Foundation of China (Grant No. Z1100221)Fundamental Research Funds for the Central Universities of China (Grant No. 2009QNA4031)
文摘The prediction of the multiscale flow in the Knudsen pump is important for understanding its pumping mechanism.However,there is little research on such interesting multiscale phenomenon in the Knudsen pumps.In this paper,a novel numerical analysis method combining the direct simulation Monte Carlo（DSMC） method with the smoothed particle hydrodynamics（SPH） method is presented for simulating the multiscale flow,which is often encountered in the application of the Knudsen pumps.Validity and accuracy of the new method are given by comparing its results with that of the previous research.Using the coupled multiscale approach,the rarefaction and the temperature drive are studied,which are two main factors on the performance of the Knudsen pumps.To investigate the effect of rarefaction on the performance of the Knudsen pump,various pump operation pressures are compared.The flow characteristics and pumping ability at different rarefaction are analyzed,and the phenomenon of the multiscale flow is also discussed.Several cases with different linear or nonlinear temperature gradients are set to investigate the effect of temperature gradient on the performance of the Knudsen pump.The flow characteristics of the Knudsen pump such as the velocity,pressure increase,and the mass flowrate are presented.A unique phenomenon,the reverse transpiration effect caused by the nonlinear temperature gradient is studied,and the reason of the significant pressure increase in the pump channel is also analyzed.Since the multiscale gas flow is widely encountered in the microflow systems,the above method and its results can also be greatly beneficial and provide significant insights for the design of the MEMS devices.
基金supported by the National Natural Science Foundation of China (No. 10472101)the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20070335184)
文摘Given the definition of the reference Knudsen number for micro gas journal bearings,the range in the number is related to the viscosity of air at different temperatures. A modified Reynolds equation for micro gas journal bearings based on Burgdorfer's first-order slip boundary condition is proposed that takes into account the gas rarefaction effect. The finite difference method (FDM) is adopted to solve the modified Reynolds equation to obtain the pressure profiles,load capacities and attitude angles for micro gas journal bearings at different reference Knudsen numbers,bearing numbers and journal eccentricity ratios. Numerical analysis shows that pressure profiles and non-dimensional load capacities decrease markedly as gas rarefaction in-creases. Attitude angles change conversely,and when the eccentricity ratio is less than 0.6,the attitude angles rise slightly and the influence of the reference Knudsen number is not marked. In addition,the effect of gas rarefaction on the non-dimensional load capacity and attitude angle decreases with smaller bearing numbers.
基金supported by the National Natural Science Foundation of China(11627901,11872118).
文摘Shock wave is emitted into the plate and sphere when a sphere hypervelocity impacts onto a thin plate.The fragmentation and phase change of the material caused by the propagation and unloading of shock wave could result in the formation of debris cloud eventually.Propagation models are deduced based on one-dimensional shock wave theory and the geometry of sphere,which uses elliptic equations(corresponding to ellipsoid equations in physical space)to describe the propagation of shock wave and the rarefaction wave.The“Effective thickness”is defined as the critical plate thickness that ensures the rarefaction wave overtake the shock wave at the back of the sphere.The“Effective thickness”is directly related to the form of the debris cloud.The relation of the“Effective thickness”and the“Optimum thickness”is also discussed.The impacts of Al spheres onto Al plates are simulated within SPH to verify the propagation models and associated theories.The results show that the wave fronts predicted by the propagation models are closer to the simulation result at higher impact velocity.The curvatures of the wave fronts decrease with the increase of impact velocities.The predicted“Effective thickness”is consistent with the simulation results.The analysis about the shock wave propagation and unloading in this paper can provide a new sight and inspiration for the quantitative study of hypervelocity impact and space debris protection.
基金Sponsored by the National Natural Science Foundation of China (10671116,10871199, and 10001023)Hou Yingdong Fellowship (81004), The China Scholarship Council, Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, Natural Science Foundation of Guangdong (06027210 and 000804)Natural Science Foundation of Guangdong Education Bureau (200030)
文摘In this article, we get non-selfsimilar elementary waves of the conservation laws in another kind of view, which is different from the usual self-similar transformation. The solution has different global structure. This article is divided into three parts. The first part is introduction. In the second part, we discuss non-selfsimilar elementary waves and their interactions of a class of twodimensional conservation laws. In this case, we consider the case that the initial discontinuity is parabola with u＋ 〉 0, while explicit non-selfsirnilar rarefaction wave can be obtained. In the second part, we consider the solution structure of case u＋ 〈 0. The new solution structures are obtained by the interactions between different elementary waves, and will continue to interact with other states. Global solutions would be very different from the situation of one dimension.
文摘This paper is concerned with the stability of the rarefaction wave for the Burgers equationwhere 0 ≤ a < 1/4p (q is determined by (2.2)). Roughly speaking, under the assumption that u_ < u+, the authors prove the existence of the global smooth solution to the Cauchy problem (I), also find the solution u(x, t) to the Cauchy problem (I) satisfying sup |u(x, t) -uR(x/t)| → 0 as t → ∞, where uR(x/t) is the rarefaction wave of the non-viscous Burgersequation ut + f(u)x = 0 with Riemann initial data u(x, 0) =
基金supported by 973 Key program and the Key Program from Beijing Educational Commission with No. KZ200910028002Program for New Century Excellent Talents in University (NCET)+4 种基金Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (PHR-IHLB)The research of Sheng partially supported by NSFC (10671120)Shanghai Leading Academic Discipline Project: J50101The research of Zhang partially supported by NSFC (10671120)The research of Zheng partially supported by NSF-DMS-0603859
文摘In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections： 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.
基金The research was supported by three grants from the Key Project of the Natural Science Foundation of China (10431060)the Key Project of Chinese Ministry of Education (104128)the South-Central University For Nationalities Natural Science Foundation of China (YZY05008)
文摘In this article, authors study the Cauch problem for a model of hyperbolic-elliptic coupled system derived from the one-dimensional system of the rudiating gas. By considering the initial data as a small disturbances of rarefaction wave of inviscid Burgers equation, the global existence of the solution to the corresponding Cauchy problem and asymptotic stability of rarefaction wave is proved. The analysis is based on a priori estimates and L^2-energy method.
基金Project supported by National Natural Science Foundation of China(Grant No .10271072)
文摘In this paper, the Riemann solutions for scalar conservation laws with discontinuous flux function were constructed. The interactions of elementary waves of the conservation laws were concerned, and the numerical simulations were given.
基金supported by NSFC Grant No.11171153supported by NSFC Grant No.11322106supported by the Fundamental Research Funds for the Central Universities No.2015ZCQ-LY-01 and No.BLX2015-27
文摘In this article, we investigate the global stability of the wave patterns with the superposition of viscous contact wave and rarefaction wave for the one-dimensional compressible Navier-Stokes equations with a free boundary. It is shown that for the ideal polytropic gas, the superposition of the viscous contact wave with rarefaction wave is nonlinearly stable for the free boundary problem under the large initial perturbations for any γ 〉 1 with V being the adiabatic exponent provided that the wave strength is suitably small.
