The Boltzmann equations for Fermi-Dirac particles and Bose-Einstein particles, both in the absence of external force fields, are combined into a more general form called the Boltzmann equation with quantum effects (BQ...The Boltzmann equations for Fermi-Dirac particles and Bose-Einstein particles, both in the absence of external force fields, are combined into a more general form called the Boltzmann equation with quantum effects (BQE). It is assumed that the initial data f(x,v,0) satisfies 0≤f(x,v,0)≤cΦ(x,v,0) for a positive constant c and certain types of control functions Φ(x,v,t). Then within a given function space B(Φ), we prove that f(x+tv,v,t) uniformly converges to f ∞(x,v) in a certain norm where f ∞(x,v)= limt→∞f(x+tv,v,t) and different initial data determines different long time limits.展开更多
This paper is devoted to the existence and long time behavior of the global classical solution to Fokker-Planck-Boltzmann equation with initial data near the absolute Maxwellian.
By establishing concept an transient solutions of general nonlinear systems converging to its equilibrium set, long-time behavior of solutions for cellular neural network systems is studied. A stability condition in g...By establishing concept an transient solutions of general nonlinear systems converging to its equilibrium set, long-time behavior of solutions for cellular neural network systems is studied. A stability condition in generalized sense is obtained. This result reported has an important guide to concrete neural network designs.展开更多
We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantu...We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantum number, jz is the z-component of angular momentum） state is {（1 - K/G）/[1 - （K/G）2j＋1]}（K/G）^α-1 as t → ＋∞, which coincides with the fact that when K/G 〉 1, the larger the a is, the larger the probability of the atom being in the α-th state （the lower excited state） is. We also consider the case for some possible generaizations of the atomic master equation.展开更多
The asymptotic behavior of the solutions to a class of pseudoparabolic viscous diffusion equation with periodic initial condition is studied by using the spectral method. The semidiscrete Fourier approximate solution ...The asymptotic behavior of the solutions to a class of pseudoparabolic viscous diffusion equation with periodic initial condition is studied by using the spectral method. The semidiscrete Fourier approximate solution of the problem is constructed and the error estimation between spectral approximate solution and exact solution on large time is also obtained. The existence of the approximate attractor AN and the upper semicontinuity d（AN,A） → 0 are proved.展开更多
In order to investigate the time-dependent behaviors of deep hard rocks in the diversion tunnel of Jinping II hydropower station, uniaxial creep tests were carried out by using the triaxial testing machine RC-2000. Th...In order to investigate the time-dependent behaviors of deep hard rocks in the diversion tunnel of Jinping II hydropower station, uniaxial creep tests were carried out by using the triaxial testing machine RC-2000. The axial compressive load was applied step by step and each creep stage was kept for over several days. Test results show that： （1） The lateral deformation of rock specimens is 2-3 times the axial compressive deformation and accelerates drastically before damage, which may be employed as an indicator to predict the excavation-induced instability of rocks. （2） The resultant deformation changes from compression to expansion when the Poisson＇s ratio is larger than 0.5, indicating the starting point of damage. （3） In the step-loading stages, the Poisson＇s ratio approximately remains constant; under constantly imposed load, the Poisson＇s ratio changes with elapsed time, growing continuously before the specimen is damaged. （4） When the applied load reaches a certain threshold value, the rock deteriorates with time, and the strength of rocks approximately has a negative exponent relation with time. （5） The failure modes of the deep marble are different in long- and short-term loading conditions. Under the condition of short-term loading, the specimen presents a mode of tensile failure; while under the condition of long-term loading, the specimen presents a mode of shear failure, followed by tensile failure.展开更多
The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,th...The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann(or periodic)boundary conditions.Furthermore,by a logarithmic Sobolev inequality,it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.展开更多
In this paper, we investigate the global existence and long time behavior of strong solutions for compressible nematic liquid crystal flows in threedimensional whole space. The global existence of strong solutions is ...In this paper, we investigate the global existence and long time behavior of strong solutions for compressible nematic liquid crystal flows in threedimensional whole space. The global existence of strong solutions is obtained by the standard energy method under the condition that the initial data are close to the constant equilibrium state in H2-framework. If the initial datas in Ll-norm are finite additionally, the optimal time decay rates of strong solutions are established. With the help of Fourier splitting method, one also establishes optimal time decay rates for the higher order spatial derivatives of director.展开更多
基金Supported by the Tsinghua U niversity Science Fund
文摘The Boltzmann equations for Fermi-Dirac particles and Bose-Einstein particles, both in the absence of external force fields, are combined into a more general form called the Boltzmann equation with quantum effects (BQE). It is assumed that the initial data f(x,v,0) satisfies 0≤f(x,v,0)≤cΦ(x,v,0) for a positive constant c and certain types of control functions Φ(x,v,t). Then within a given function space B(Φ), we prove that f(x+tv,v,t) uniformly converges to f ∞(x,v) in a certain norm where f ∞(x,v)= limt→∞f(x+tv,v,t) and different initial data determines different long time limits.
基金supported by the National Natural Science Foundation of China(No.11301094)supported by the National Natural Science Foundation of China(No.11171228,11231006 and 11225102)the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions(No.CIT&TCD20140323)
文摘This paper is devoted to the existence and long time behavior of the global classical solution to Fokker-Planck-Boltzmann equation with initial data near the absolute Maxwellian.
文摘By establishing concept an transient solutions of general nonlinear systems converging to its equilibrium set, long-time behavior of solutions for cellular neural network systems is studied. A stability condition in generalized sense is obtained. This result reported has an important guide to concrete neural network designs.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11105133)
文摘We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantum number, jz is the z-component of angular momentum） state is {（1 - K/G）/[1 - （K/G）2j＋1]}（K/G）^α-1 as t → ＋∞, which coincides with the fact that when K/G 〉 1, the larger the a is, the larger the probability of the atom being in the α-th state （the lower excited state） is. We also consider the case for some possible generaizations of the atomic master equation.
基金This work was supported by the National Science Foundation of China(10271034)
文摘The asymptotic behavior of the solutions to a class of pseudoparabolic viscous diffusion equation with periodic initial condition is studied by using the spectral method. The semidiscrete Fourier approximate solution of the problem is constructed and the error estimation between spectral approximate solution and exact solution on large time is also obtained. The existence of the approximate attractor AN and the upper semicontinuity d（AN,A） → 0 are proved.
基金Supported by the National Natural Science Foundation of China(50909092)the Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences (Z000802)the Natural Science Foundation of Hubei Province (2009CDB120)
文摘In order to investigate the time-dependent behaviors of deep hard rocks in the diversion tunnel of Jinping II hydropower station, uniaxial creep tests were carried out by using the triaxial testing machine RC-2000. The axial compressive load was applied step by step and each creep stage was kept for over several days. Test results show that： （1） The lateral deformation of rock specimens is 2-3 times the axial compressive deformation and accelerates drastically before damage, which may be employed as an indicator to predict the excavation-induced instability of rocks. （2） The resultant deformation changes from compression to expansion when the Poisson＇s ratio is larger than 0.5, indicating the starting point of damage. （3） In the step-loading stages, the Poisson＇s ratio approximately remains constant; under constantly imposed load, the Poisson＇s ratio changes with elapsed time, growing continuously before the specimen is damaged. （4） When the applied load reaches a certain threshold value, the rock deteriorates with time, and the strength of rocks approximately has a negative exponent relation with time. （5） The failure modes of the deep marble are different in long- and short-term loading conditions. Under the condition of short-term loading, the specimen presents a mode of tensile failure; while under the condition of long-term loading, the specimen presents a mode of shear failure, followed by tensile failure.
基金Project supported by the National Natural Science Foundation of China(Nos.10631020,10401019)the Basic Research Grant of Tsinghua University.
文摘The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann(or periodic)boundary conditions.Furthermore,by a logarithmic Sobolev inequality,it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.
文摘In this paper, we investigate the global existence and long time behavior of strong solutions for compressible nematic liquid crystal flows in threedimensional whole space. The global existence of strong solutions is obtained by the standard energy method under the condition that the initial data are close to the constant equilibrium state in H2-framework. If the initial datas in Ll-norm are finite additionally, the optimal time decay rates of strong solutions are established. With the help of Fourier splitting method, one also establishes optimal time decay rates for the higher order spatial derivatives of director.
