A two-layer model based on the linearized time-independent atmospheric dynamical equations is proposed in this paper. The analytical solutions of the vertical, the horizontal motions and the potential temperature fiel...A two-layer model based on the linearized time-independent atmospheric dynamical equations is proposed in this paper. The analytical solutions of the vertical, the horizontal motions and the potential temperature field induced by the anthropogenic source of urban surface heating are obtained, therefore the heat island circulation existing in unstable boundary layer is verified theoretically. From the analytical solutions, some conclusions can be drawn. (1) The vertical motion induced by urban heat island consists of two parts, namely, the cross-hill wave and the lee wave; (2) The cross-hill wave only exists in the unstable boundary layer, and varies with height according to exponential function law; (3) The vertical motion induced by heat island reaches the maximum at the top of the unstable boundary layer; (4) The wave generated by heat island not only propogates to the downwind district but also travels to the upwind area; (5) γ≠0 is not the necessary condition of the lee wave generation.展开更多
Determining whether a quantum state is separable or inseparable （entangled） is a problem of fundamental importance in quantum science and has attracted much attention since its first recognition by Einstein, Podolsk...Determining whether a quantum state is separable or inseparable （entangled） is a problem of fundamental importance in quantum science and has attracted much attention since its first recognition by Einstein, Podolsky and Rosen [Phys. Rev., 1935, 47： 777] and SchrSdinger [Naturwissenschaften, 1935, 23： 807-812, 823-828, 844-849]. In this paper, we propose a successive approximation method （SAM） for this problem, which approximates a given quantum state by a so-called separable state： if the given states is separable, this method finds its rank-one components and the associated weights; otherwise, this method finds the distance between the given state to the set of separable states, which gives information about the degree of entanglement in the system. The key task per iteration is to find a feasible descent direction, which is equivalent to finding the largest M-eigenvalue of a fourth-order tensor. We give a direct method for this problem when the dimension of the tensor is 2 and a heuristic cross-hill method for cases of high dimension. Some numerical results and experiences are presented.展开更多
文摘A two-layer model based on the linearized time-independent atmospheric dynamical equations is proposed in this paper. The analytical solutions of the vertical, the horizontal motions and the potential temperature field induced by the anthropogenic source of urban surface heating are obtained, therefore the heat island circulation existing in unstable boundary layer is verified theoretically. From the analytical solutions, some conclusions can be drawn. (1) The vertical motion induced by urban heat island consists of two parts, namely, the cross-hill wave and the lee wave; (2) The cross-hill wave only exists in the unstable boundary layer, and varies with height according to exponential function law; (3) The vertical motion induced by heat island reaches the maximum at the top of the unstable boundary layer; (4) The wave generated by heat island not only propogates to the downwind district but also travels to the upwind area; (5) γ≠0 is not the necessary condition of the lee wave generation.
文摘Determining whether a quantum state is separable or inseparable （entangled） is a problem of fundamental importance in quantum science and has attracted much attention since its first recognition by Einstein, Podolsky and Rosen [Phys. Rev., 1935, 47： 777] and SchrSdinger [Naturwissenschaften, 1935, 23： 807-812, 823-828, 844-849]. In this paper, we propose a successive approximation method （SAM） for this problem, which approximates a given quantum state by a so-called separable state： if the given states is separable, this method finds its rank-one components and the associated weights; otherwise, this method finds the distance between the given state to the set of separable states, which gives information about the degree of entanglement in the system. The key task per iteration is to find a feasible descent direction, which is equivalent to finding the largest M-eigenvalue of a fourth-order tensor. We give a direct method for this problem when the dimension of the tensor is 2 and a heuristic cross-hill method for cases of high dimension. Some numerical results and experiences are presented.
