Homogeneous matrices are widely used to represent geometric transformations in computer graphics, with interpo- lation between those matrices being of high interest for computer animation. Many approaches have been pr...Homogeneous matrices are widely used to represent geometric transformations in computer graphics, with interpo- lation between those matrices being of high interest for computer animation. Many approaches have been proposed to address this problem, including computing matrix curves from curves in Euclidean space by registration, representing one-parameter curves on manifold by rational representations, changing subdivisional methods generating curves in Euclidean space to corresponding methods working for matrix curve generation, and variational methods. In this paper, we propose a scheme to generate rational one-parameter matrix curves based on exponential map for interpolation, and demonstrate how to obtain higher smoothness from existing curves. We also give an iterative technique for rapid computing of these curves. We take the computation as solving an ordinary differential equation on manifold numerically by a generalized Euler method. Furthermore, we give this algorithm’s bound of the error and prove that the bound is proportional to the shift length when the shift length is sufficiently small. Compared to direct computation of the matrix functions, our Euler solution is faster.展开更多
We construct a particle-number （n）-resolved master equation （ME） approach under the self-consistent Born approximation （SCBA） for quantum transport through mesoscopic systems. The formulation is essentially non-...We construct a particle-number （n）-resolved master equation （ME） approach under the self-consistent Born approximation （SCBA） for quantum transport through mesoscopic systems. The formulation is essentially non-Markovian and incorporates the interplay of the multi-tunneling processes and many-body correlations. The proposed n-SCBA-ME goes beyond the scope of the Born- Markov master equation, being applicable to transport under small bias voltage, in non-Markovian regime and with strong Coulomb correlations. For steady state, it can recover not only the exact result of noninteracting transport under arbitrary voltages, but also the challenging nonequilibrium Kondo effect. Moreover, the n-SCBA-ME approach is efficient for the study of shot noise. We demonstrate the application by a couple of representative examples, including particularly the nonequilibrium Kondo system.展开更多
Two stochastic models are derived for a susceptible-infectious-susceptible epidemic spreading through a metapopulation： a continuous time Markov chain （CTMC） model and an It6 stochastic differential equation （SDE...Two stochastic models are derived for a susceptible-infectious-susceptible epidemic spreading through a metapopulation： a continuous time Markov chain （CTMC） model and an It6 stochastic differential equation （SDE） model. The stochastic models are numerically compared. Close agreement suggests that computationally intense CTMC simulations can be approximated by simpler SDE simulations. Differential equations for the moments of the SDE probability distribution are also derived, the steady states are solved numerically using a moment closure technique, and these results are compared to simulations. The moment closure technique only coarsely approximates simulation results. The effect of model parameters on stability of the disease-free equilibrium is also numerically investigated.展开更多
In this work, the ft values of the 0+ →0+ superallowed Fermi beta decays have been investigated. In the calculations, the shell model has been modified by Pyatov's restoration method because of the isospin breaki...In this work, the ft values of the 0+ →0+ superallowed Fermi beta decays have been investigated. In the calculations, the shell model has been modified by Pyatov's restoration method because of the isospin breaking and the transition matrix elements have been found by means of the quasi-particle random phase approximation (QRPA).展开更多
基金Project (No. 200038) partially supported by FANEDD, China
文摘Homogeneous matrices are widely used to represent geometric transformations in computer graphics, with interpo- lation between those matrices being of high interest for computer animation. Many approaches have been proposed to address this problem, including computing matrix curves from curves in Euclidean space by registration, representing one-parameter curves on manifold by rational representations, changing subdivisional methods generating curves in Euclidean space to corresponding methods working for matrix curve generation, and variational methods. In this paper, we propose a scheme to generate rational one-parameter matrix curves based on exponential map for interpolation, and demonstrate how to obtain higher smoothness from existing curves. We also give an iterative technique for rapid computing of these curves. We take the computation as solving an ordinary differential equation on manifold numerically by a generalized Euler method. Furthermore, we give this algorithm’s bound of the error and prove that the bound is proportional to the shift length when the shift length is sufficiently small. Compared to direct computation of the matrix functions, our Euler solution is faster.
基金supported by the National Natural Science Foundation of Chinathe Major State Basic Research Project of China(Grant Nos.2011CB808502 and 2012CB932704)+2 种基金the Fundamental Research Funds for the Central Universities of Chinasupportedby the Program for Excellent Young Teachers in Hangzhou Normal Universitythe National Natural Science Foundation of China(Grant No.11274085)
文摘We construct a particle-number （n）-resolved master equation （ME） approach under the self-consistent Born approximation （SCBA） for quantum transport through mesoscopic systems. The formulation is essentially non-Markovian and incorporates the interplay of the multi-tunneling processes and many-body correlations. The proposed n-SCBA-ME goes beyond the scope of the Born- Markov master equation, being applicable to transport under small bias voltage, in non-Markovian regime and with strong Coulomb correlations. For steady state, it can recover not only the exact result of noninteracting transport under arbitrary voltages, but also the challenging nonequilibrium Kondo effect. Moreover, the n-SCBA-ME approach is efficient for the study of shot noise. We demonstrate the application by a couple of representative examples, including particularly the nonequilibrium Kondo system.
文摘Two stochastic models are derived for a susceptible-infectious-susceptible epidemic spreading through a metapopulation： a continuous time Markov chain （CTMC） model and an It6 stochastic differential equation （SDE） model. The stochastic models are numerically compared. Close agreement suggests that computationally intense CTMC simulations can be approximated by simpler SDE simulations. Differential equations for the moments of the SDE probability distribution are also derived, the steady states are solved numerically using a moment closure technique, and these results are compared to simulations. The moment closure technique only coarsely approximates simulation results. The effect of model parameters on stability of the disease-free equilibrium is also numerically investigated.
文摘In this work, the ft values of the 0+ →0+ superallowed Fermi beta decays have been investigated. In the calculations, the shell model has been modified by Pyatov's restoration method because of the isospin breaking and the transition matrix elements have been found by means of the quasi-particle random phase approximation (QRPA).
