Aim To study the Lie symmetries and conserved quantities of holonomic mechanical systems in terms of qnasi-coordinates. Methods The definition of an infinitesimal generator for the holonomic mechanical systems in te...Aim To study the Lie symmetries and conserved quantities of holonomic mechanical systems in terms of qnasi-coordinates. Methods The definition of an infinitesimal generator for the holonomic mechanical systems in terms of quasi-coordinates was given. Lie's method of the invariance of ordinary differential equations under infinitesimal transformations was used. Results and Conclusion The determining equations of the Lie symmetries of holonomic mechanical systems in terms of quassi-coordinates are established. The structure equation and the form of conserved quantities are obtained. An example to illustrate the applicaiton of the result is given.展开更多
Aim To study the Lie symmetries and conserved quantities of the dynamical equationsof relative motion for holonomic mechanical systems. Methods Lie's method of the invariance of ordinary differential equations u...Aim To study the Lie symmetries and conserved quantities of the dynamical equationsof relative motion for holonomic mechanical systems. Methods Lie's method of the invariance of ordinary differential equations under infinitesimal transformations was used. Results and Conclusion The determining equaiton of the Lie symmetries for the dynamical equationS of relative motion is established.The structure quation and the form conserved quantities are obtained. An example iD illustrate the application of the result is given.展开更多
The Lie symmetries of nonholonomic mechanical systems are corsidered. Some defmi tions and criteria on the Lie symmetries, and the conservation laws of the systems are given.And some examples to illustrate the applic...The Lie symmetries of nonholonomic mechanical systems are corsidered. Some defmi tions and criteria on the Lie symmetries, and the conservation laws of the systems are given.And some examples to illustrate the application of the results are provided.展开更多
This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are es...This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are established. The definition of the Lie symmetrical transformations of the systems is given, which only depends upon the infinitesimal transformations of groups for the generalized coordinates. The conserved quantity is directly constructed in terms of the Lie symmetry of the systems. The condition under which the Lie symmetry can lead to the conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.展开更多
Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformati...Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformations to establish the determining equations and the restriction equations of the Lie symmetries of the systems. Results and Conclusion the structure equation and the form of conserved quantities were obtained. An example was given to illustrate the application of the result.展开更多
To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relati...To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relation between the form invariance and the Noether symmetry was established.展开更多
Nineβ‐cyclodextrin derivatives containing an amino group were synthesized via nucleophilic sub‐stitution from mono(6‐O‐p‐tolylsulfonyl)‐β‐cyclodextrin and used in asymmetric biomimetic Mi‐chael addition re...Nineβ‐cyclodextrin derivatives containing an amino group were synthesized via nucleophilic sub‐stitution from mono(6‐O‐p‐tolylsulfonyl)‐β‐cyclodextrin and used in asymmetric biomimetic Mi‐chael addition reactions in water at room temperature. The mechanism responsible for the moder‐ate activity and enantioselectivity of the β‐cyclodextrin derivatives was explored using nuclear magnetic resonance spectroscopy, namely 2D 1H rotating‐frame overhauser effect spectroscopy (ROESY), ultraviolet absorption spectroscopy, and quantum chemical calculations, which provide a useful technique for investigating the formation of inclusion complexes. The effects of the pH of the reaction medium, theβ‐cyclodextrin derivative dosage, the structure of the modifying amino group, and various substrates on the yield and enantioselectivity were investigated. The results indicated that these factors had an important effect on the enantiomeric excess (ee) in the reaction system. Experiments using a competitor for inclusion complex formation showed that a hydrophobic cavity is necessary for enantioselective Michael addition. A comparison of the reactions using 4‐nitro‐β‐nitrostyrene and 2‐nitro‐β‐nitrostyrene showed that steric hindrance improved the enan‐tioselectivity. This was verified by the optimized geometries obtained from quantum chemical cal‐culations. An ee of 71%was obtained in the asymmetric Michael addition of cyclohexanone and 2‐nitro‐β‐nitrostyrene, using (S)‐2‐aminomethylpyrrolidine‐modified β‐CD as the catalyst, in an aqueous buffer solution, i.e., CH3COONa‐HCl (pH 7.5).展开更多
The form invariance of Routh equations in holonomic systems is studied. The definition and criterion for the form invariance under the infinitesimal transformations are given. The relation of the form invariance with ...The form invariance of Routh equations in holonomic systems is studied. The definition and criterion for the form invariance under the infinitesimal transformations are given. The relation of the form invariance with the Noether symmetry and the Lie symmetry is discussed.展开更多
Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity.Though this is abeautiful idea, which may resolve many long standing problems in the theories of gravity, it also raises many otherprob...Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity.Though this is abeautiful idea, which may resolve many long standing problems in the theories of gravity, it also raises many otherproblems.In this article I will comment on some of the problems of Verlinde’s proposal with special emphasis on thethermodynamical origin of the principle of relativity.It is found that there is a large group of hidden symmetries ofthermodynamics, which contains the Poincare group of the spacetime for which space is emergent.This explains thethermodynamic origin of the principle of relativity.展开更多
Tolerance is imperative for seamless integration of CAD/CAM(Computer Aided Disign/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types,...Tolerance is imperative for seamless integration of CAD/CAM(Computer Aided Disign/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types, the relations between which are very complicated. In addition, the different principles of tolerance make study of tolerance difficult; and there may be various meanings or interpretation for the same type of tolerance because of the literal definition. In this work, latest unambiguous mathematical definition was applied to study, explain and clarify: (1) the formation and representation of tolerance zone, and (2) the formation and representation of variational elements; after which, the mathematical models of symmetry of different tolerance principles and different interpretations were derived. An example is given to illustrate the application of these models in tolerance analysis.展开更多
We investigate the influence of a perpendicular magnetic field on a bound polaron near the interface of a polar-polar semiconductor with Rashba effect. The external magnetic field strongly changes the ground state bin...We investigate the influence of a perpendicular magnetic field on a bound polaron near the interface of a polar-polar semiconductor with Rashba effect. The external magnetic field strongly changes the ground state binding energy of the polaron and the Rashba spin-orbit (SO) interaction originating from the inversion asymmetry in the heterostructure splits the ground state binding energy of the bound polaron. In this paper, we have shown how the ground state binding energy will be with the change of the external magnetic field, the location of a single impurity, the wave vector of the electron and the electron areal density, taking into account the SO coupling. Due to the presence of the phonons, whose energy gives negative contribution to the polaron's, the spin-splitting states of the bound polaron are more stable, and we find that in the condition of week magnetic field, the Zeeaman effect can be neglected.展开更多
Based on the concept of adiabatic invariant, the perturbation and adiabatic invariants of the Mei symmetry for nonholonomic mechanical systems are studied. The exact invariants of the Mei symmetry for the system witho...Based on the concept of adiabatic invariant, the perturbation and adiabatic invariants of the Mei symmetry for nonholonomic mechanical systems are studied. The exact invariants of the Mei symmetry for the system without perturbation are given. The perturbation to the Mei symmetry is discussed and the adiabatic invariants of the Mei symmetry for the perturbed system are obtained.展开更多
A new present weather identifier(PWI) based on occlusion and scattering techniques is presented in the study. The present weather parameters are detectable by the meteorological optical range(MOR) approximately up to ...A new present weather identifier(PWI) based on occlusion and scattering techniques is presented in the study. The present weather parameters are detectable by the meteorological optical range(MOR) approximately up to 50 km and by droplets with diameters ranging from 0.125 mm to 22 mm with velocities up to 16 m s-1. The MOR error is less than 8% for the MOR within 10 km and less than 15% for farther distances. Moreover, the size errors derived from various positions of the light sheet by the particles were checked within ± 0.1 mm ± 5%. The comparison shows that the MOR, in a sudden shower event, is surprisingly consistent with those of the sentry visibility sensors(SVS) with a correlation coefficient up to 98%. For the rain amounts derived from the size and velocity of the droplets, the daily sums by the PWI agree within 10% of those by the Total Rain Weighing Sensor(TRwS205) and the rain gauge. Combined with other sensors such as temperature, humidity, and wind, the PWI can serve as a present weather sensor to distinguish several weather types such as fog, haze, mist, rain, hail, and drizzle.展开更多
In three-dimensional quantum electrodynamics (QED3) with a massive gauge boson, we investigate the coupled Dyson-Schwinger equations for the fermion and photon propagators in the rainbow approximation, and obtain the ...In three-dimensional quantum electrodynamics (QED3) with a massive gauge boson, we investigate the coupled Dyson-Schwinger equations for the fermion and photon propagators in the rainbow approximation, and obtain the critical gauge boson mass for various numbers of the fermion flavors. A comparision with the previous results is presented.展开更多
To research the influence of asymmetric brake shoe forces(ABSF)induced by braking failure on the dynamic performance of six-axle locomotive,the static equilibrium model of three-axle bogie and dynamic model for locomo...To research the influence of asymmetric brake shoe forces(ABSF)induced by braking failure on the dynamic performance of six-axle locomotive,the static equilibrium model of three-axle bogie and dynamic model for locomotive are established.The coupling vibration equations of axle hung motor and wheelset are derived.For the air braking,the influence mechanism of ABSF on the wheel-rail asymmetric motion and force characteristics are discussed.It can be found that if the ABSF is applied in the front wheelset,all the wheelsets move laterally in the same direction.Once the ABSF occurs in the middle or rear one,other wheelsets may move laterally towards the opposite direction.The motion amplitude and direction of all wheelsets strictly depend on the resultant moment of suspension yawing moment and brake shoe asymmetric moment.For the asymmetric braking,the free lateral gap of axle-box could increase the wheelset motion amplitude,but could not change the moving direction.In both the straight line and curve,the ABSF may lead to wheelset misaligning motion,intensify the wheel-rail lateral dynamic interaction and deteriorate wheel-rail contact state.Especially for the steering wheelsets,the asymmetric braking increases the wheelset attack angle significantly,which forms the worst braking condition.展开更多
In this paper the Lie symmetry and conserved quantities for nonholonomic Vacco dynamical systems are studied. The determining equation of the Lie symmetry for the system is given. The general Hojman conserved quantity...In this paper the Lie symmetry and conserved quantities for nonholonomic Vacco dynamical systems are studied. The determining equation of the Lie symmetry for the system is given. The general Hojman conserved quantity and the Lutzky conserved quantity deduced from the symmetry are obtained.展开更多
In this paper, we study potential symmetries to certain systems of nonlinear diffusion equations. Thosesystems have physical applications in soil science, mathematical biology, and invariant curve flows in R^3. Lie po...In this paper, we study potential symmetries to certain systems of nonlinear diffusion equations. Thosesystems have physical applications in soil science, mathematical biology, and invariant curve flows in R^3. Lie point symmetries of the potential system, which cannot be projected to vector fields of the given dependent and independent variables, yield potential symmetries. The class of the system that admits potential symmetries is expanded.展开更多
This paper presents a study on potential instability and spiral structure of unstable rain clusters.First,we develop a linearized non-axisymmetrical mathematic model for rain clusters in circular cylindrical coordinat...This paper presents a study on potential instability and spiral structure of unstable rain clusters.First,we develop a linearized non-axisymmetrical mathematic model for rain clusters in circular cylindrical coordinates and acquire its analytic solution.Second,we discuss the potential instability of non-axisymmetrical rain clusters.Finally,we conclude that spiral structures can exist in rain clusters.Our analysis indicates that potential instability occurs when humid stratification coefficient is less than zero.Unstable growth rate increases with the increase of the absolute value for humid stratification coefficient.The simpler the vertical structure of perturbation,the thicker the inversion layer;additionally,the smaller the radius of the rain clusters,the larger the unstable growth rate.Simulation results agree well with those from observation and forecast.The spiral structure simulated by our model is similar to a radar echo,suggesting that rain clusters with spiral structures can occur in the atmosphere.In addition,they are generally close to the model solution in this work.展开更多
Unidirectional transport of a particle in a spatially periodic and symmetric potential under a periodic force with broken temporal symmetry is studied. With a collaboration of the potential field and the asymmetric ac...Unidirectional transport of a particle in a spatially periodic and symmetric potential under a periodic force with broken temporal symmetry is studied. With a collaboration of the potential field and the asymmetric ac force, a dc current can be observed. Resonant current steps are found for a finite period of the ac force. A phase diagram of these resonant steps is given. Stochastic-resonance-like directional transport induced by thermal noises is revealed.展开更多
We study the functional separation of variables to the nonlinear heat equation: ut = (A(x)D(u)ux^n)x+ B(x)Q(u), Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables...We study the functional separation of variables to the nonlinear heat equation: ut = (A(x)D(u)ux^n)x+ B(x)Q(u), Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables is studied by using the group foliation method. A classification of the equation which admits the functional separable solutions is performed. As a consequence, some solutions to the resulting equations are obtained.展开更多
文摘Aim To study the Lie symmetries and conserved quantities of holonomic mechanical systems in terms of qnasi-coordinates. Methods The definition of an infinitesimal generator for the holonomic mechanical systems in terms of quasi-coordinates was given. Lie's method of the invariance of ordinary differential equations under infinitesimal transformations was used. Results and Conclusion The determining equations of the Lie symmetries of holonomic mechanical systems in terms of quassi-coordinates are established. The structure equation and the form of conserved quantities are obtained. An example to illustrate the applicaiton of the result is given.
文摘Aim To study the Lie symmetries and conserved quantities of the dynamical equationsof relative motion for holonomic mechanical systems. Methods Lie's method of the invariance of ordinary differential equations under infinitesimal transformations was used. Results and Conclusion The determining equaiton of the Lie symmetries for the dynamical equationS of relative motion is established.The structure quation and the form conserved quantities are obtained. An example iD illustrate the application of the result is given.
文摘The Lie symmetries of nonholonomic mechanical systems are corsidered. Some defmi tions and criteria on the Lie symmetries, and the conservation laws of the systems are given.And some examples to illustrate the application of the results are provided.
文摘This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are established. The definition of the Lie symmetrical transformations of the systems is given, which only depends upon the infinitesimal transformations of groups for the generalized coordinates. The conserved quantity is directly constructed in terms of the Lie symmetry of the systems. The condition under which the Lie symmetry can lead to the conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.
文摘Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformations to establish the determining equations and the restriction equations of the Lie symmetries of the systems. Results and Conclusion the structure equation and the form of conserved quantities were obtained. An example was given to illustrate the application of the result.
文摘To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relation between the form invariance and the Noether symmetry was established.
基金supported by the National Natural Science Foundation of China (21425627,21376279)~~
文摘Nineβ‐cyclodextrin derivatives containing an amino group were synthesized via nucleophilic sub‐stitution from mono(6‐O‐p‐tolylsulfonyl)‐β‐cyclodextrin and used in asymmetric biomimetic Mi‐chael addition reactions in water at room temperature. The mechanism responsible for the moder‐ate activity and enantioselectivity of the β‐cyclodextrin derivatives was explored using nuclear magnetic resonance spectroscopy, namely 2D 1H rotating‐frame overhauser effect spectroscopy (ROESY), ultraviolet absorption spectroscopy, and quantum chemical calculations, which provide a useful technique for investigating the formation of inclusion complexes. The effects of the pH of the reaction medium, theβ‐cyclodextrin derivative dosage, the structure of the modifying amino group, and various substrates on the yield and enantioselectivity were investigated. The results indicated that these factors had an important effect on the enantiomeric excess (ee) in the reaction system. Experiments using a competitor for inclusion complex formation showed that a hydrophobic cavity is necessary for enantioselective Michael addition. A comparison of the reactions using 4‐nitro‐β‐nitrostyrene and 2‐nitro‐β‐nitrostyrene showed that steric hindrance improved the enan‐tioselectivity. This was verified by the optimized geometries obtained from quantum chemical cal‐culations. An ee of 71%was obtained in the asymmetric Michael addition of cyclohexanone and 2‐nitro‐β‐nitrostyrene, using (S)‐2‐aminomethylpyrrolidine‐modified β‐CD as the catalyst, in an aqueous buffer solution, i.e., CH3COONa‐HCl (pH 7.5).
文摘The form invariance of Routh equations in holonomic systems is studied. The definition and criterion for the form invariance under the infinitesimal transformations are given. The relation of the form invariance with the Noether symmetry and the Lie symmetry is discussed.
基金Supported by the National Natural Science Foundation of China under Grant No.10875059
文摘Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity.Though this is abeautiful idea, which may resolve many long standing problems in the theories of gravity, it also raises many otherproblems.In this article I will comment on some of the problems of Verlinde’s proposal with special emphasis on thethermodynamical origin of the principle of relativity.It is found that there is a large group of hidden symmetries ofthermodynamics, which contains the Poincare group of the spacetime for which space is emergent.This explains thethermodynamic origin of the principle of relativity.
文摘Tolerance is imperative for seamless integration of CAD/CAM(Computer Aided Disign/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types, the relations between which are very complicated. In addition, the different principles of tolerance make study of tolerance difficult; and there may be various meanings or interpretation for the same type of tolerance because of the literal definition. In this work, latest unambiguous mathematical definition was applied to study, explain and clarify: (1) the formation and representation of tolerance zone, and (2) the formation and representation of variational elements; after which, the mathematical models of symmetry of different tolerance principles and different interpretations were derived. An example is given to illustrate the application of these models in tolerance analysis.
基金The project supported by National Natural Science Foundation of China under Grant No. 90305026
文摘We investigate the influence of a perpendicular magnetic field on a bound polaron near the interface of a polar-polar semiconductor with Rashba effect. The external magnetic field strongly changes the ground state binding energy of the polaron and the Rashba spin-orbit (SO) interaction originating from the inversion asymmetry in the heterostructure splits the ground state binding energy of the bound polaron. In this paper, we have shown how the ground state binding energy will be with the change of the external magnetic field, the location of a single impurity, the wave vector of the electron and the electron areal density, taking into account the SO coupling. Due to the presence of the phonons, whose energy gives negative contribution to the polaron's, the spin-splitting states of the bound polaron are more stable, and we find that in the condition of week magnetic field, the Zeeaman effect can be neglected.
文摘Based on the concept of adiabatic invariant, the perturbation and adiabatic invariants of the Mei symmetry for nonholonomic mechanical systems are studied. The exact invariants of the Mei symmetry for the system without perturbation are given. The perturbation to the Mei symmetry is discussed and the adiabatic invariants of the Mei symmetry for the perturbed system are obtained.
基金supported by Automatic Observation System for Cloud, Visibility and Weather Phenomena (Grant No. GYHY200806031)Carbon Satellites Verification Systems and Comprehensive Observations (Grant Nos. GJHZ1207 and XDA05040302)
文摘A new present weather identifier(PWI) based on occlusion and scattering techniques is presented in the study. The present weather parameters are detectable by the meteorological optical range(MOR) approximately up to 50 km and by droplets with diameters ranging from 0.125 mm to 22 mm with velocities up to 16 m s-1. The MOR error is less than 8% for the MOR within 10 km and less than 15% for farther distances. Moreover, the size errors derived from various positions of the light sheet by the particles were checked within ± 0.1 mm ± 5%. The comparison shows that the MOR, in a sudden shower event, is surprisingly consistent with those of the sentry visibility sensors(SVS) with a correlation coefficient up to 98%. For the rain amounts derived from the size and velocity of the droplets, the daily sums by the PWI agree within 10% of those by the Total Rain Weighing Sensor(TRwS205) and the rain gauge. Combined with other sensors such as temperature, humidity, and wind, the PWI can serve as a present weather sensor to distinguish several weather types such as fog, haze, mist, rain, hail, and drizzle.
文摘In three-dimensional quantum electrodynamics (QED3) with a massive gauge boson, we investigate the coupled Dyson-Schwinger equations for the fermion and photon propagators in the rainbow approximation, and obtain the critical gauge boson mass for various numbers of the fermion flavors. A comparision with the previous results is presented.
基金Projects(52072249,51605315)supported by the National Natural Science Foundation of ChinaProject(E2018210052)supported by the Natural Science Foundation of Hebei Province,ChinaProject(TPL1707)supported by the Open Funds for the State Key Laboratory of Traction Power,China。
文摘To research the influence of asymmetric brake shoe forces(ABSF)induced by braking failure on the dynamic performance of six-axle locomotive,the static equilibrium model of three-axle bogie and dynamic model for locomotive are established.The coupling vibration equations of axle hung motor and wheelset are derived.For the air braking,the influence mechanism of ABSF on the wheel-rail asymmetric motion and force characteristics are discussed.It can be found that if the ABSF is applied in the front wheelset,all the wheelsets move laterally in the same direction.Once the ABSF occurs in the middle or rear one,other wheelsets may move laterally towards the opposite direction.The motion amplitude and direction of all wheelsets strictly depend on the resultant moment of suspension yawing moment and brake shoe asymmetric moment.For the asymmetric braking,the free lateral gap of axle-box could increase the wheelset motion amplitude,but could not change the moving direction.In both the straight line and curve,the ABSF may lead to wheelset misaligning motion,intensify the wheel-rail lateral dynamic interaction and deteriorate wheel-rail contact state.Especially for the steering wheelsets,the asymmetric braking increases the wheelset attack angle significantly,which forms the worst braking condition.
文摘In this paper the Lie symmetry and conserved quantities for nonholonomic Vacco dynamical systems are studied. The determining equation of the Lie symmetry for the system is given. The general Hojman conserved quantity and the Lutzky conserved quantity deduced from the symmetry are obtained.
基金The project supported by National Natural Science Foundation of China under Grant No.10671156the Program for New CenturyExcellent Talents in Universities under Grant No.NCET-04-0968
文摘In this paper, we study potential symmetries to certain systems of nonlinear diffusion equations. Thosesystems have physical applications in soil science, mathematical biology, and invariant curve flows in R^3. Lie point symmetries of the potential system, which cannot be projected to vector fields of the given dependent and independent variables, yield potential symmetries. The class of the system that admits potential symmetries is expanded.
基金National Natural Science Foundation of China.(4097503141005074)
文摘This paper presents a study on potential instability and spiral structure of unstable rain clusters.First,we develop a linearized non-axisymmetrical mathematic model for rain clusters in circular cylindrical coordinates and acquire its analytic solution.Second,we discuss the potential instability of non-axisymmetrical rain clusters.Finally,we conclude that spiral structures can exist in rain clusters.Our analysis indicates that potential instability occurs when humid stratification coefficient is less than zero.Unstable growth rate increases with the increase of the absolute value for humid stratification coefficient.The simpler the vertical structure of perturbation,the thicker the inversion layer;additionally,the smaller the radius of the rain clusters,the larger the unstable growth rate.Simulation results agree well with those from observation and forecast.The spiral structure simulated by our model is similar to a radar echo,suggesting that rain clusters with spiral structures can occur in the atmosphere.In addition,they are generally close to the model solution in this work.
文摘Unidirectional transport of a particle in a spatially periodic and symmetric potential under a periodic force with broken temporal symmetry is studied. With a collaboration of the potential field and the asymmetric ac force, a dc current can be observed. Resonant current steps are found for a finite period of the ac force. A phase diagram of these resonant steps is given. Stochastic-resonance-like directional transport induced by thermal noises is revealed.
基金National Natural Science Foundation of China under Grant No.10671156the Program for New Century Excellent Talents in Universities under Grant No.NCET-04-0968
文摘We study the functional separation of variables to the nonlinear heat equation: ut = (A(x)D(u)ux^n)x+ B(x)Q(u), Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables is studied by using the group foliation method. A classification of the equation which admits the functional separable solutions is performed. As a consequence, some solutions to the resulting equations are obtained.