The molecular dynamics simulations are performed to show that in aque- ous environments, a short single-walled carbon nanotube （SWCNT） guided by a long SWCNT, either inside or outside the longer tube, is capable of ...The molecular dynamics simulations are performed to show that in aque- ous environments, a short single-walled carbon nanotube （SWCNT） guided by a long SWCNT, either inside or outside the longer tube, is capable of moving along the nanotube axis unidirectionally in an electric field perpendicular to the carbon nanotube （CNT） axis with the linear gradient. The design suggests a new way of molecule transportation or mass delivery. To reveal the mechanism behind this phenomenon, the free energy profiles of the system are calculated by the method of the potential of mean force （PMF）.展开更多
In this paper the system of Reynolds equations of the multi-scaled atmospheric motions is set up based on the con- cept of decomposing the meteorological elements into multi-scale disturbances.It is proved to be true ...In this paper the system of Reynolds equations of the multi-scaled atmospheric motions is set up based on the con- cept of decomposing the meteorological elements into multi-scale disturbances.It is proved to be true that the Reynolds exchange term in the averaged motion is equal to the sum of averaged nonlinear terms in all sub-averaged motions.In order to avoid the higher order closure in Eulerian approaches,a new K-theory based on the multi-scaled Reynolds equations is given in which the subscale motions are described by Langevin equation as the air particles are moving in the Eulerian average background.From the new K-theory are derived the momentum,heat and mass exchange coefficients as the functions of statistical variables such as variances and Lagrangian time scales of velocity,temperature and other meteorological elements in disturbances.The new K-theory also expounds the causes for the differences be- tween the exchange coefficients of one element and another and gives the ambient conditions in which the buoyancy and/or Coriolis force Will build the chaotic disturbances into the orderly gradient of mean values of the corresponding elements.In consequence the K-theory can be used to explain some of negative viscosity phenomena in atmospheric mo- tions.展开更多
This study developed a theoretical approach to understanding how a set amount of a granular bed is discharged from a tilted rotary kiln （an empty cylinder） once its particle size distribution （PSD） is known and sl...This study developed a theoretical approach to understanding how a set amount of a granular bed is discharged from a tilted rotary kiln （an empty cylinder） once its particle size distribution （PSD） is known and slumping motion occurs. The basis of the study is that the preparation of material for thermal treat- ment inside a rotary kiln （pyrolysis, gasification, and]or combustion） involves shredding to a desired particle size. Further mechanical stress results from the feeder screws moving material from storage toward the reactor. The most common PSDs found in uniform size reduction processes and mechanical stresses are Gaussian, log-normal, and Rosin-Rammler, of which the latter best fits the PSD in our study. Different particle diameters in the distribution result in an axial segregation when a slumping motion occurs, resulting in particles of different diameters leaving the kiln at different instants. After develop- ing the model, the theoretical data showed good agreement when compared with experimental results obtained from downloading previously shredded carbonaceous material from a rotary kiln at 2 and 4 rpm rotational speeds. The mean residence times at steady state were determined for both rotational speeds and showed good agreement with data provided in the literature.展开更多
The purpose of the present work is to construct new geometrical models for motion of plane curve by Darboux transformations. We get nonlinear partial differential equations (PDE). We have obtained the exact solutions ...The purpose of the present work is to construct new geometrical models for motion of plane curve by Darboux transformations. We get nonlinear partial differential equations (PDE). We have obtained the exact solutions of the resulting equations using symmetry groups method. Also, the Gaussian and mean curvatures of Monge form of the soliton surfaces have been calculated and discussed.展开更多
In this paper,we study a new class of equations called mean-field backward stochastic differential equations(BSDEs,for short)driven by fractional Brownian motion with Hurst parameter H>1/2.First,the existence and u...In this paper,we study a new class of equations called mean-field backward stochastic differential equations(BSDEs,for short)driven by fractional Brownian motion with Hurst parameter H>1/2.First,the existence and uniqueness of this class of BSDEs are obtained.Second,a comparison theorem of the solutions is established.Third,as an application,we connect this class of BSDEs with a nonlocal partial differential equation(PDE,for short),and derive a relationship between the fractional mean-field BSDEs and PDEs.展开更多
From Kaula's Earth gravitational potential written in classical orbital elements, the unified ideal model of mean motion resonance of artificial satellites due to geopotential perturbations is developed in this pa...From Kaula's Earth gravitational potential written in classical orbital elements, the unified ideal model of mean motion resonance of artificial satellites due to geopotential perturbations is developed in this paper first, through a suitable sequence of canonical transformations constructed by implicit functions. This unified ideal orbital resonance model is valid for all the commensurabilities between the rotational angular velocity of the Earth and the angular velocities of mean orbital motion of artificial satellites with arbitrary inclination and small eccentricity, and can be also transformed into Garfinkel's general expression of ideal resonance problem. Then 1/1 resonance of the 24-hour satellite with arbitrary inclination and small eccentricity is analyzed under the effect of harmonics of J2 and J 22 of the geopotential, based on the unified ideal model of mean motion resonance. The analytical expressions of the libration period and libration half width of the 1/1 resonance of the 24-hour satellite with arbitrary inclination and small eccentricity are presented.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11372175 and 11272197)the Research Fund for the Doctoral Program of Higher Education of China(No.20103108110004)the Innovation Program of Shanghai Municipality Education Commission(No.14ZZ095)
文摘The molecular dynamics simulations are performed to show that in aque- ous environments, a short single-walled carbon nanotube （SWCNT） guided by a long SWCNT, either inside or outside the longer tube, is capable of moving along the nanotube axis unidirectionally in an electric field perpendicular to the carbon nanotube （CNT） axis with the linear gradient. The design suggests a new way of molecule transportation or mass delivery. To reveal the mechanism behind this phenomenon, the free energy profiles of the system are calculated by the method of the potential of mean force （PMF）.
文摘In this paper the system of Reynolds equations of the multi-scaled atmospheric motions is set up based on the con- cept of decomposing the meteorological elements into multi-scale disturbances.It is proved to be true that the Reynolds exchange term in the averaged motion is equal to the sum of averaged nonlinear terms in all sub-averaged motions.In order to avoid the higher order closure in Eulerian approaches,a new K-theory based on the multi-scaled Reynolds equations is given in which the subscale motions are described by Langevin equation as the air particles are moving in the Eulerian average background.From the new K-theory are derived the momentum,heat and mass exchange coefficients as the functions of statistical variables such as variances and Lagrangian time scales of velocity,temperature and other meteorological elements in disturbances.The new K-theory also expounds the causes for the differences be- tween the exchange coefficients of one element and another and gives the ambient conditions in which the buoyancy and/or Coriolis force Will build the chaotic disturbances into the orderly gradient of mean values of the corresponding elements.In consequence the K-theory can be used to explain some of negative viscosity phenomena in atmospheric mo- tions.
文摘This study developed a theoretical approach to understanding how a set amount of a granular bed is discharged from a tilted rotary kiln （an empty cylinder） once its particle size distribution （PSD） is known and slumping motion occurs. The basis of the study is that the preparation of material for thermal treat- ment inside a rotary kiln （pyrolysis, gasification, and]or combustion） involves shredding to a desired particle size. Further mechanical stress results from the feeder screws moving material from storage toward the reactor. The most common PSDs found in uniform size reduction processes and mechanical stresses are Gaussian, log-normal, and Rosin-Rammler, of which the latter best fits the PSD in our study. Different particle diameters in the distribution result in an axial segregation when a slumping motion occurs, resulting in particles of different diameters leaving the kiln at different instants. After develop- ing the model, the theoretical data showed good agreement when compared with experimental results obtained from downloading previously shredded carbonaceous material from a rotary kiln at 2 and 4 rpm rotational speeds. The mean residence times at steady state were determined for both rotational speeds and showed good agreement with data provided in the literature.
文摘The purpose of the present work is to construct new geometrical models for motion of plane curve by Darboux transformations. We get nonlinear partial differential equations (PDE). We have obtained the exact solutions of the resulting equations using symmetry groups method. Also, the Gaussian and mean curvatures of Monge form of the soliton surfaces have been calculated and discussed.
基金supported by the National Key R&D Program of China (Grant No. 2018YFA0703900)the National Natural Science Foundation of China (Grant Nos. 11871309 and 11371226)+3 种基金supported by China Postdoctoral Science Foundation (Grant No. 2019M660968)Southern University of Science and Technology Start up fund Y01286233supported by Southern University of Science and Technology Start up fund Y01286120the National Natural Science Foundation of China (Grants Nos. 61873325,11831010)
文摘In this paper,we study a new class of equations called mean-field backward stochastic differential equations(BSDEs,for short)driven by fractional Brownian motion with Hurst parameter H>1/2.First,the existence and uniqueness of this class of BSDEs are obtained.Second,a comparison theorem of the solutions is established.Third,as an application,we connect this class of BSDEs with a nonlocal partial differential equation(PDE,for short),and derive a relationship between the fractional mean-field BSDEs and PDEs.
基金supported by the National Natural Science Foundation of China (Grant nos. 11033009, 11125315 and 11103086)
文摘From Kaula's Earth gravitational potential written in classical orbital elements, the unified ideal model of mean motion resonance of artificial satellites due to geopotential perturbations is developed in this paper first, through a suitable sequence of canonical transformations constructed by implicit functions. This unified ideal orbital resonance model is valid for all the commensurabilities between the rotational angular velocity of the Earth and the angular velocities of mean orbital motion of artificial satellites with arbitrary inclination and small eccentricity, and can be also transformed into Garfinkel's general expression of ideal resonance problem. Then 1/1 resonance of the 24-hour satellite with arbitrary inclination and small eccentricity is analyzed under the effect of harmonics of J2 and J 22 of the geopotential, based on the unified ideal model of mean motion resonance. The analytical expressions of the libration period and libration half width of the 1/1 resonance of the 24-hour satellite with arbitrary inclination and small eccentricity are presented.
