The equation of motion of a viscoelastic rod of density rod p is considered when the Constitutive Relationships contains fractional derivatives （in the Riemann-Liouville sense） of order β, 0 ≤ β ≤ 1. The solutio...The equation of motion of a viscoelastic rod of density rod p is considered when the Constitutive Relationships contains fractional derivatives （in the Riemann-Liouville sense） of order β, 0 ≤ β ≤ 1. The solution of this equation is given in a general case. It is shown that for the limit values of the derivative index ,β, i.e. when β = 0 or β = 1, the general solution gives rise to classical solutions of hyperbolic and parabolic equations.展开更多
Downtime due to adverse wave conditions for vessels at berth is an important commercial aspect in the planning and development of a sea port or a berthing terminal. This paper describes a practical technique for preli...Downtime due to adverse wave conditions for vessels at berth is an important commercial aspect in the planning and development of a sea port or a berthing terminal. This paper describes a practical technique for preliminary assessment of operational downtime at a proposed bulk terminal. Time-series wind and wave data at an offshore location was purchased. Numerical modelling was then carried out using the MIKE21 SW （spectral wave） model developed by DHI （Deutsches Hydrographisches Institut） to transform these offshore waves into inshore in order to derive wave conditions at the berth. Both wind-waves and swell-waves were considered. Waves affecting the head and beam of a vessel were considered separately for a wide range of vessel sizes with DT （displacement tonnage） ranging from 5,000 tons to 〉 200,000 tons. The limiting wave height H5% was used. Operational downtime was also calculated using significant wave height, Hs as a criterion with limits ofHs = 1.0 m for beam seas and Hs = 1.5 m for head seas. The methodology and lessons learnt from the study can be applied for the development of any sea port worldwide.展开更多
Measuring the top coal movement and abutment pressure about Teaching ThirdMine that belonged to the National Energy Investment and Development.It shows that thetop coal's strong compression occurs 6 m in front of ...Measuring the top coal movement and abutment pressure about Teaching ThirdMine that belonged to the National Energy Investment and Development.It shows that thetop coal's strong compression occurs 6 m in front of the face, the top coal is in front of sideabutment pressure concentration increase area at this time, and the top coal horizontaldisplacement increase rapidly.Also analyzed the top coal mechanical properties, and thetop coal under abutment pressure turned into block state.Finally, analyzed the top coalfailure mechanism and the structure of the mechanical model, and also made a theoreticalanalysis of the top coal's ultimate bearing capacity.展开更多
Functional limit theorems for scaled occupation time fluctuations of a sequence of generalized branching particle systems in Rd with anisotropic space motions and strongly degenerated splitting abilities are studied i...Functional limit theorems for scaled occupation time fluctuations of a sequence of generalized branching particle systems in Rd with anisotropic space motions and strongly degenerated splitting abilities are studied in the cases of critical and intermediate dimensions. The results show that the limit processes are time-independent measure-valued Wiener processes with simple spatial structure.展开更多
In this paper, we prove some limit theorems for killed Brownian motion during its life time. The emphases are on quasi-stationarity and quasi-ergodicity and related problems. On one hand, using an eigenfunction expans...In this paper, we prove some limit theorems for killed Brownian motion during its life time. The emphases are on quasi-stationarity and quasi-ergodicity and related problems. On one hand, using an eigenfunction expansion for the transition density, we prove the existence and uniqueness of both quasi-stationary distribution (qsd) and mean ratio quasi-stationary distribution (mrqsd). The later is shown to be closely related to laws of large numbers (LLN) and to quasi-ergodicity. We further show that the mrqsd is the unique stationary distribution of a certain limiting ergodic diffusion process of the BM conditioned on not having been killed. We also show that a phase transition occurs from mrqsd to qsd. On the other hand, we study the large deviation behavior related to the above problems. A key observation is that the mrqsd is the unique minimum of certain large deviation rate function. We further prove that the limiting diffusion process also satisfies a large deviation principle with the rate function attaining its unique minimum at the mrqsd. These give interpretations of the mrqsd from different points of view, and establish some intrinsic connections among the above topics. Some general results concerning Yaglom limit, moment convergence and LLN are also obtained.展开更多
We study tile local linear estimator for tile drift coefficient of stochastic differential equations driven by α-stable Levy motions observed at discrete instants. Under regular conditions, we derive the weak consis-...We study tile local linear estimator for tile drift coefficient of stochastic differential equations driven by α-stable Levy motions observed at discrete instants. Under regular conditions, we derive the weak consis- tency and central limit theorem of the estimator. Compared with Nadaraya-Watson estimator, the local linear estimator has a bias reduction whether the kernel function is symmetric or not under different schemes. A silnu- lation study demonstrates that the local linear estimator performs better than Nadaraya-Watson estimator, especially on the boundary.展开更多
The dependence of dislocation mobility on stress is the fundamental ingredient for the deformation in crystalline materials. Strength and ductility, the two most important properties characterizing mechanical behavior...The dependence of dislocation mobility on stress is the fundamental ingredient for the deformation in crystalline materials. Strength and ductility, the two most important properties characterizing mechanical behavior of crystalline metals, are in general governed by dislocation motion. Recording the position of a moving dislocation in a short time window is still challenging, and direct observations which enable us to deduce the speed-stress relationship of dislocations are still missing. Using large-scale molecular dynamics simulations, we obtain the motion of an obstacle-free twinning partial dislocation in face centred cubic crystals with spatial resolution at the angstrom scale and picosecond temporal information. The dislocation exhibits two limiting speeds: the first is subsonic and occurs when the resolved shear stress is on the order of hundreds of megapascal. While the stress is raised to gigapascal level, an abrupt jump of dislocation velocity occurs, from subsonic to supersonic regime. The two speed limits are governed respectively by the local transverse and longitudinal phonons associated with the stressed dislocation, as the two types of phonons facilitate dislocation gliding at different stress levels.展开更多
文摘The equation of motion of a viscoelastic rod of density rod p is considered when the Constitutive Relationships contains fractional derivatives （in the Riemann-Liouville sense） of order β, 0 ≤ β ≤ 1. The solution of this equation is given in a general case. It is shown that for the limit values of the derivative index ,β, i.e. when β = 0 or β = 1, the general solution gives rise to classical solutions of hyperbolic and parabolic equations.
文摘Downtime due to adverse wave conditions for vessels at berth is an important commercial aspect in the planning and development of a sea port or a berthing terminal. This paper describes a practical technique for preliminary assessment of operational downtime at a proposed bulk terminal. Time-series wind and wave data at an offshore location was purchased. Numerical modelling was then carried out using the MIKE21 SW （spectral wave） model developed by DHI （Deutsches Hydrographisches Institut） to transform these offshore waves into inshore in order to derive wave conditions at the berth. Both wind-waves and swell-waves were considered. Waves affecting the head and beam of a vessel were considered separately for a wide range of vessel sizes with DT （displacement tonnage） ranging from 5,000 tons to 〉 200,000 tons. The limiting wave height H5% was used. Operational downtime was also calculated using significant wave height, Hs as a criterion with limits ofHs = 1.0 m for beam seas and Hs = 1.5 m for head seas. The methodology and lessons learnt from the study can be applied for the development of any sea port worldwide.
文摘Measuring the top coal movement and abutment pressure about Teaching ThirdMine that belonged to the National Energy Investment and Development.It shows that thetop coal's strong compression occurs 6 m in front of the face, the top coal is in front of sideabutment pressure concentration increase area at this time, and the top coal horizontaldisplacement increase rapidly.Also analyzed the top coal mechanical properties, and thetop coal under abutment pressure turned into block state.Finally, analyzed the top coalfailure mechanism and the structure of the mechanical model, and also made a theoreticalanalysis of the top coal's ultimate bearing capacity.
基金supported by National Natural Science Foundation of China (Grant No. 10901054)
文摘Functional limit theorems for scaled occupation time fluctuations of a sequence of generalized branching particle systems in Rd with anisotropic space motions and strongly degenerated splitting abilities are studied in the cases of critical and intermediate dimensions. The results show that the limit processes are time-independent measure-valued Wiener processes with simple spatial structure.
基金supported by National Natural Science Foundation of China(Grant No. 10971253)
文摘In this paper, we prove some limit theorems for killed Brownian motion during its life time. The emphases are on quasi-stationarity and quasi-ergodicity and related problems. On one hand, using an eigenfunction expansion for the transition density, we prove the existence and uniqueness of both quasi-stationary distribution (qsd) and mean ratio quasi-stationary distribution (mrqsd). The later is shown to be closely related to laws of large numbers (LLN) and to quasi-ergodicity. We further show that the mrqsd is the unique stationary distribution of a certain limiting ergodic diffusion process of the BM conditioned on not having been killed. We also show that a phase transition occurs from mrqsd to qsd. On the other hand, we study the large deviation behavior related to the above problems. A key observation is that the mrqsd is the unique minimum of certain large deviation rate function. We further prove that the limiting diffusion process also satisfies a large deviation principle with the rate function attaining its unique minimum at the mrqsd. These give interpretations of the mrqsd from different points of view, and establish some intrinsic connections among the above topics. Some general results concerning Yaglom limit, moment convergence and LLN are also obtained.
基金supported by National Natural Science Foundation of China(Grant Nos.11171303 and 11071213)the Specialized Research Fund for the Doctor Program of Higher Education(Grant No.20090101110020)
文摘We study tile local linear estimator for tile drift coefficient of stochastic differential equations driven by α-stable Levy motions observed at discrete instants. Under regular conditions, we derive the weak consis- tency and central limit theorem of the estimator. Compared with Nadaraya-Watson estimator, the local linear estimator has a bias reduction whether the kernel function is symmetric or not under different schemes. A silnu- lation study demonstrates that the local linear estimator performs better than Nadaraya-Watson estimator, especially on the boundary.
基金supported by the National Natural Science Foundation of China(Grant No.11425211)
文摘The dependence of dislocation mobility on stress is the fundamental ingredient for the deformation in crystalline materials. Strength and ductility, the two most important properties characterizing mechanical behavior of crystalline metals, are in general governed by dislocation motion. Recording the position of a moving dislocation in a short time window is still challenging, and direct observations which enable us to deduce the speed-stress relationship of dislocations are still missing. Using large-scale molecular dynamics simulations, we obtain the motion of an obstacle-free twinning partial dislocation in face centred cubic crystals with spatial resolution at the angstrom scale and picosecond temporal information. The dislocation exhibits two limiting speeds: the first is subsonic and occurs when the resolved shear stress is on the order of hundreds of megapascal. While the stress is raised to gigapascal level, an abrupt jump of dislocation velocity occurs, from subsonic to supersonic regime. The two speed limits are governed respectively by the local transverse and longitudinal phonons associated with the stressed dislocation, as the two types of phonons facilitate dislocation gliding at different stress levels.
