We investigate the integrability of the Rabi model,which is traditionally viewed as not Yang–Baxter-integrable despite its solvability.Building on efforts by Bogoliubov and Kulish(2013 J.Math.Sci.19214–30),Amico et ...We investigate the integrability of the Rabi model,which is traditionally viewed as not Yang–Baxter-integrable despite its solvability.Building on efforts by Bogoliubov and Kulish(2013 J.Math.Sci.19214–30),Amico et al(2007 Nucl.Phys.B 787283–300),and Batchelor and Zhou(2015 Phys.Rev.A 91053808),who explored special limiting cases of the model,we develop a spin–boson interaction Hamiltonian under more general boundary conditions,particularly focusing on open boundary conditions with off-diagonal terms.Our approach maintains the direction of the spin in the z direction and also preserves the boson particle number operator a^(†)a,marking a progression beyond previous efforts that have primarily explored reduced forms of the Rabi model from Yang–Baxter algebra.We also address the presence of‘unwanted’quadratic boson terms a^(2) and a^(†2),which share coefficients with the boson particle number operator.Interestingly,these terms vanish when spectral parameter u=±θ_(s),simplifying the model to a limiting case of operator-valued twists,a scenario previously discussed by Batchelor and Zhou(2015 Phys.Rev.A 91053808).展开更多
We developed a Global Ocean Circulation and Tide Model （GOCTM） with coarse grids in the open deep ocean degrading ‘smoothly’ into the highly resolved China Seas （CS） of refined grids to study the tides and circu...We developed a Global Ocean Circulation and Tide Model （GOCTM） with coarse grids in the open deep ocean degrading ‘smoothly’ into the highly resolved China Seas （CS） of refined grids to study the tides and circulation there.GOCTM is based on the framework of the Finite Volume approach for better mass conservation through improved transports across the discrete individual control volume.It also takes a full advantage of the geometric flexibility of unstructured mesh using a realistic global topography including the Arctic Ocean.The CS are given a special focus by refining the unstructured grids,but they are embedded into global domain naturally.Furthermore,GOCTM not only successfully avoids the treatment of the open boundaries,but also optimizes the trade-off between computational cost and model accuracy.Meanwhile,GOCTM is driven by the astronomical tide-generating potential and the secondary tide-generating potential directly,together with the wind stress and heat flux.GOCTM succeeds in reproducing the global eight principal tidal harmonic constants.Particularly,the simulated tidal results in the CS are improved compared to some other regional models with the discrepancy of 3.9 cm for M 2 tide.This idea of GOCTM can also be referred for other regional ocean study.展开更多
Two-dimensional tidal open boundary conditions of the M2 constituent in the Bohai and Yellow Seas(BYS) have been estimated by assimilating T/P altimeter data.During inversion,independent point(IP) strategy was used,in...Two-dimensional tidal open boundary conditions of the M2 constituent in the Bohai and Yellow Seas(BYS) have been estimated by assimilating T/P altimeter data.During inversion,independent point(IP) strategy was used,in which several IPs on the open boundary is assumed,values at these IPs can be optimized with an adjoint method,and those at other grid points are determined by linearly interpolating the values at IPs.The reasonability and feasibility of the model are tested by ideal twin experiments.In the practical experiment(PE) after assimilation,the cost function may reach 1% or less of its initial value.Mean absolute errors in amplitude and phase can be less than 5 cm and 5°,respectively,and the obtained co-chart can show the character of the M2 constituent in the BYS.The results of the PE indicate that using only two IPs on the open boundary can yield better simulated results.展开更多
N-component Bariev model for correlated hopping under open boundary conditions in one dimension is studied in the framework of Bethe ansatz method. The energy spectrum and the related Bethe ansatz equations are obtained.
In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition （OSC）. As applications, we discuss a self-simila...In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition （OSC）. As applications, we discuss a self-similar Cantor set satisfying OSC and give a simple method for computing its exact Hausdorff measure.展开更多
Open boundary conditions （OBCs） for a regional ocean model that can be integrated stably over a long timeframe, as well as satisfy the volume, heat and salinity conservation constraints, were developed. First, the i...Open boundary conditions （OBCs） for a regional ocean model that can be integrated stably over a long timeframe, as well as satisfy the volume, heat and salinity conservation constraints, were developed. First, the idea that the inward and outward flux information can be treated separately in the OBCs was adopted. Second, in order to maintain the property that the volume, heat and salinity remains conserved in the simulation domain, conservation constraints were added to the OBCs, and an inverse method utilized to solve the constraint equations. Ideal experiments were designed to investigate the conservation property, and the OBCs were found to work efficiently to maintain the volume, heat and salinity conservation. It was found that simulations were comparable to observations when the OBCs were applied to a regional ocean model.展开更多
A significant improvement of the open boundary condition which was originally studied by Engquist and Majda is given.The method given here is applicable without limitation of the angle between the direction of the inc...A significant improvement of the open boundary condition which was originally studied by Engquist and Majda is given.The method given here is applicable without limitation of the angle between the direction of the incident wave and the normal to the boundary.It also improves the precision of the method from order one to two.The test examples show that this method is much better than the method mentioned above.展开更多
In Rels. [2-4] there is an Adaptive. Open Boundary Condition (AOBC) designed for transient waves which overcomes the limitation of the existing Open BoundaryCondition (OBC) and can be used for the cases of waves with...In Rels. [2-4] there is an Adaptive. Open Boundary Condition (AOBC) designed for transient waves which overcomes the limitation of the existing Open BoundaryCondition (OBC) and can be used for the cases of waves with arbitrary incidentangles. In this article a new family of high order AOBC has been designed on the basisof the above mentioned AOBC with the first order.In comparison with all other OBC with the same order, this new family of AOBC has the highest precision.展开更多
The reliability of electric supply to consumers is one of the most important factors that determine the requirements imposed on modem utility companies. This paper presents the results of investigation by computer sof...The reliability of electric supply to consumers is one of the most important factors that determine the requirements imposed on modem utility companies. This paper presents the results of investigation by computer software of the overvoltages resulting from a ferroresonance conditions in MV networks at open phase operating condition with and without connection to earth on source and load sides of distribution transformer. This overvoltage may reach 4.2 pu on one of the HV side of transformer unswitched phases. The results of the study show that ferroresonance overvoltage may be controlled by replacing fuses with circuit breakers on HV side to ensure switching-off all phases. Insertion of resistor or reactor in the neutral of source and loadsides of the transformer with 5% active load will help in suppressing overvoltages.展开更多
Recently Lou and Wu obtained the formulas of pointwise dimensions of some Moran measures on Moran sets in Rd under the strong separation condition.In this paper,we prove that the result is still true under the open se...Recently Lou and Wu obtained the formulas of pointwise dimensions of some Moran measures on Moran sets in Rd under the strong separation condition.In this paper,we prove that the result is still true under the open set condition.Due to the lack of the strong separation condition,our approach is essentially different from that used by Lou and Wu.We also obtain the formulas of the Hausdorff and packing dimensions of the Moran measures and discuss some interesting examples.展开更多
The entanglement in an anisotropic spin-1 Heisenberg chain with a uniform magnetic field is investigated. The ground-state entanglement will undergo two different kinds of transitions when the anisotropy △ and the am...The entanglement in an anisotropic spin-1 Heisenberg chain with a uniform magnetic field is investigated. The ground-state entanglement will undergo two different kinds of transitions when the anisotropy △ and the amplitude of the magnetic field B are varied. The thermal entanglement of the nearest neighbour always declines when B increases no matter what the value of the anisotropy is. It is very interesting to note that the entanglement of the next-nearest neighbour can increase to a maximum at a certain magnetic field. Regardless of the boundary condition, the nearestneighbour entanglement always decreases and approaches to a constant value when the size of the system is very large. The constant value of open boundary condition is much larger than that of periodic boundary condition.展开更多
A characteristic like model is presented to calculate the two dimensional flow in open channels with finite or infinite dimensions. The comparisons between the computational results and experimental data show the mo...A characteristic like model is presented to calculate the two dimensional flow in open channels with finite or infinite dimensions. The comparisons between the computational results and experimental data show the model to be robust in simulating two dimensional unsteady flows. The comparisons also show the effectiveness of the open boundary condition in simulation of wave propagation process in an infinite domain with computational domain of finite dimension.展开更多
In this paper, a computational case was employed to describe thecomputational procedure for inversing the tidal level open boundary conditions using an analyticmethod. The area for finding the solution is a circular a...In this paper, a computational case was employed to describe thecomputational procedure for inversing the tidal level open boundary conditions using an analyticmethod. The area for finding the solution is a circular area with a circular arc with the openingangle 60°-being the open boundary and the other circular arc being the solid wall boundary.Proceeding from the reestablished elliptic partial differential equation satisfied by the tidallevel function, the extended spectrum method was used to derive the general solution of the equationfor the sea of constant depth, and the impermeable solid wall condition (the second class boundarycondition) and the adequately specified open boundary conditions were then applied to determine theundetermined coefficients of the general solution, thus obtaining the tidal level distributionfunction. In this way, both the first and second class boundary values at the solid wall boundarywere obtained. With the above boundary values as the boundary conditions, the tidal level values atthe open boundary were then inversed by means of the general solution of tidal wave equation. Thevalidity of inversion method could be verified by comparing the inversed tidal level distributionswith the originally specified open boundary values.展开更多
Let E be a self-similar set satisfying the open set condition. Professor Xu conjectures in his doctoral degree thesis that if H^8（E） 〈｜E｜^8, then for any x ∈ E, the inequality ^-D^3C（E,x）〉H^8（E）/｜E｜^8hold...Let E be a self-similar set satisfying the open set condition. Professor Xu conjectures in his doctoral degree thesis that if H^8（E） 〈｜E｜^8, then for any x ∈ E, the inequality ^-D^3C（E,x）〉H^8（E）/｜E｜^8holds, where 3 = dimH（E）. The above conjecture is negatively answered in this＇paper.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12275214,12247103,12047502)the Natural Science Basic Research Program of Shaanxi Province Grant Nos.2021JCW-19 and 2019JQ-107Shaanxi Key Laboratory for Theoretical Physics Frontiers in China.
文摘We investigate the integrability of the Rabi model,which is traditionally viewed as not Yang–Baxter-integrable despite its solvability.Building on efforts by Bogoliubov and Kulish(2013 J.Math.Sci.19214–30),Amico et al(2007 Nucl.Phys.B 787283–300),and Batchelor and Zhou(2015 Phys.Rev.A 91053808),who explored special limiting cases of the model,we develop a spin–boson interaction Hamiltonian under more general boundary conditions,particularly focusing on open boundary conditions with off-diagonal terms.Our approach maintains the direction of the spin in the z direction and also preserves the boson particle number operator a^(†)a,marking a progression beyond previous efforts that have primarily explored reduced forms of the Rabi model from Yang–Baxter algebra.We also address the presence of‘unwanted’quadratic boson terms a^(2) and a^(†2),which share coefficients with the boson particle number operator.Interestingly,these terms vanish when spectral parameter u=±θ_(s),simplifying the model to a limiting case of operator-valued twists,a scenario previously discussed by Batchelor and Zhou(2015 Phys.Rev.A 91053808).
基金The Hi-tech Research and Development Program (863) of China under contract No.2007AA09Z117the National Key Technology R&D Program under contract No.2011BAC03B02+1 种基金the National Natural Science Fund of China under contract No.40976001the National Marine Renewable Energy Program under contract Nos GHME2010ZC08,No.GHME 2010ZC11 and No.GHME2010ZC01
文摘We developed a Global Ocean Circulation and Tide Model （GOCTM） with coarse grids in the open deep ocean degrading ‘smoothly’ into the highly resolved China Seas （CS） of refined grids to study the tides and circulation there.GOCTM is based on the framework of the Finite Volume approach for better mass conservation through improved transports across the discrete individual control volume.It also takes a full advantage of the geometric flexibility of unstructured mesh using a realistic global topography including the Arctic Ocean.The CS are given a special focus by refining the unstructured grids,but they are embedded into global domain naturally.Furthermore,GOCTM not only successfully avoids the treatment of the open boundaries,but also optimizes the trade-off between computational cost and model accuracy.Meanwhile,GOCTM is driven by the astronomical tide-generating potential and the secondary tide-generating potential directly,together with the wind stress and heat flux.GOCTM succeeds in reproducing the global eight principal tidal harmonic constants.Particularly,the simulated tidal results in the CS are improved compared to some other regional models with the discrepancy of 3.9 cm for M 2 tide.This idea of GOCTM can also be referred for other regional ocean study.
基金Supported by the State Ministry of Science and Technology of China (Nos.2007AA09Z118,2008AA09A402)the National Natural Science Foundation of China(No.41076006)the Ministry of Education's 111 Project(No.B07036)
文摘Two-dimensional tidal open boundary conditions of the M2 constituent in the Bohai and Yellow Seas(BYS) have been estimated by assimilating T/P altimeter data.During inversion,independent point(IP) strategy was used,in which several IPs on the open boundary is assumed,values at these IPs can be optimized with an adjoint method,and those at other grid points are determined by linearly interpolating the values at IPs.The reasonability and feasibility of the model are tested by ideal twin experiments.In the practical experiment(PE) after assimilation,the cost function may reach 1% or less of its initial value.Mean absolute errors in amplitude and phase can be less than 5 cm and 5°,respectively,and the obtained co-chart can show the character of the M2 constituent in the BYS.The results of the PE indicate that using only two IPs on the open boundary can yield better simulated results.
文摘N-component Bariev model for correlated hopping under open boundary conditions in one dimension is studied in the framework of Bethe ansatz method. The energy spectrum and the related Bethe ansatz equations are obtained.
基金Supported in part by Education Ministry, Anhui province, China (No. KJ2008A028)
文摘In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition （OSC）. As applications, we discuss a self-similar Cantor set satisfying OSC and give a simple method for computing its exact Hausdorff measure.
基金funded by the Strategic Priority Research Program of the Chinese Academy of Sciences with Grant No.XDA11010304supported by National Natural Science Foundation of China(No.41376026 and 40776009)
文摘Open boundary conditions （OBCs） for a regional ocean model that can be integrated stably over a long timeframe, as well as satisfy the volume, heat and salinity conservation constraints, were developed. First, the idea that the inward and outward flux information can be treated separately in the OBCs was adopted. Second, in order to maintain the property that the volume, heat and salinity remains conserved in the simulation domain, conservation constraints were added to the OBCs, and an inverse method utilized to solve the constraint equations. Ideal experiments were designed to investigate the conservation property, and the OBCs were found to work efficiently to maintain the volume, heat and salinity conservation. It was found that simulations were comparable to observations when the OBCs were applied to a regional ocean model.
文摘A significant improvement of the open boundary condition which was originally studied by Engquist and Majda is given.The method given here is applicable without limitation of the angle between the direction of the incident wave and the normal to the boundary.It also improves the precision of the method from order one to two.The test examples show that this method is much better than the method mentioned above.
文摘In Rels. [2-4] there is an Adaptive. Open Boundary Condition (AOBC) designed for transient waves which overcomes the limitation of the existing Open BoundaryCondition (OBC) and can be used for the cases of waves with arbitrary incidentangles. In this article a new family of high order AOBC has been designed on the basisof the above mentioned AOBC with the first order.In comparison with all other OBC with the same order, this new family of AOBC has the highest precision.
文摘The reliability of electric supply to consumers is one of the most important factors that determine the requirements imposed on modem utility companies. This paper presents the results of investigation by computer software of the overvoltages resulting from a ferroresonance conditions in MV networks at open phase operating condition with and without connection to earth on source and load sides of distribution transformer. This overvoltage may reach 4.2 pu on one of the HV side of transformer unswitched phases. The results of the study show that ferroresonance overvoltage may be controlled by replacing fuses with circuit breakers on HV side to ensure switching-off all phases. Insertion of resistor or reactor in the neutral of source and loadsides of the transformer with 5% active load will help in suppressing overvoltages.
基金supported by National Natural Science Foundation of China (Grant No.11071082)the Fundamental Research Funds for the Central Universities,SCUT
文摘Recently Lou and Wu obtained the formulas of pointwise dimensions of some Moran measures on Moran sets in Rd under the strong separation condition.In this paper,we prove that the result is still true under the open set condition.Due to the lack of the strong separation condition,our approach is essentially different from that used by Lou and Wu.We also obtain the formulas of the Hausdorff and packing dimensions of the Moran measures and discuss some interesting examples.
文摘The entanglement in an anisotropic spin-1 Heisenberg chain with a uniform magnetic field is investigated. The ground-state entanglement will undergo two different kinds of transitions when the anisotropy △ and the amplitude of the magnetic field B are varied. The thermal entanglement of the nearest neighbour always declines when B increases no matter what the value of the anisotropy is. It is very interesting to note that the entanglement of the next-nearest neighbour can increase to a maximum at a certain magnetic field. Regardless of the boundary condition, the nearestneighbour entanglement always decreases and approaches to a constant value when the size of the system is very large. The constant value of open boundary condition is much larger than that of periodic boundary condition.
文摘A characteristic like model is presented to calculate the two dimensional flow in open channels with finite or infinite dimensions. The comparisons between the computational results and experimental data show the model to be robust in simulating two dimensional unsteady flows. The comparisons also show the effectiveness of the open boundary condition in simulation of wave propagation process in an infinite domain with computational domain of finite dimension.
文摘In this paper, a computational case was employed to describe thecomputational procedure for inversing the tidal level open boundary conditions using an analyticmethod. The area for finding the solution is a circular area with a circular arc with the openingangle 60°-being the open boundary and the other circular arc being the solid wall boundary.Proceeding from the reestablished elliptic partial differential equation satisfied by the tidallevel function, the extended spectrum method was used to derive the general solution of the equationfor the sea of constant depth, and the impermeable solid wall condition (the second class boundarycondition) and the adequately specified open boundary conditions were then applied to determine theundetermined coefficients of the general solution, thus obtaining the tidal level distributionfunction. In this way, both the first and second class boundary values at the solid wall boundarywere obtained. With the above boundary values as the boundary conditions, the tidal level values atthe open boundary were then inversed by means of the general solution of tidal wave equation. Thevalidity of inversion method could be verified by comparing the inversed tidal level distributionswith the originally specified open boundary values.
文摘Let E be a self-similar set satisfying the open set condition. Professor Xu conjectures in his doctoral degree thesis that if H^8（E） 〈｜E｜^8, then for any x ∈ E, the inequality ^-D^3C（E,x）〉H^8（E）/｜E｜^8holds, where 3 = dimH（E）. The above conjecture is negatively answered in this＇paper.
