This paper is concerned with the convergence rates to travelling waves for a relaxation model with general flux functions. Compared with former results in this direction, the main novelty in this paper lies in the fac...This paper is concerned with the convergence rates to travelling waves for a relaxation model with general flux functions. Compared with former results in this direction, the main novelty in this paper lies in the fact that the initial disturbance can be chosen large in suitable norm. Our analysis is based on the L^1-stability results obtained by C. Mascia and R. Natalini in [12].展开更多
A relaxation-rate formula is presented for the entropic lattice Boltzmann model(ELBM) - a discrete kinetic theory for hydrodynamics. The simple formula not only guarantees the discrete time H-theorem but also gives fu...A relaxation-rate formula is presented for the entropic lattice Boltzmann model(ELBM) - a discrete kinetic theory for hydrodynamics. The simple formula not only guarantees the discrete time H-theorem but also gives full consideration to the consistency with hydrodynamics. The relaxation rate calculated with the formula effectively characterizes the drastic changes of the flow fields. By using this formula, the computational cost of the ELBM is significantly reduced and the model now can be efficiently used for a broad range of applications including high Reynolds number flows.展开更多
Adaption of circadian rhythms in behavioral and physiological activities to the external light–dark cycle is achieved through the main clock, i.e., the suprachiasmatic nucleus(SCN) of the brain in mammals. It has bee...Adaption of circadian rhythms in behavioral and physiological activities to the external light–dark cycle is achieved through the main clock, i.e., the suprachiasmatic nucleus(SCN) of the brain in mammals. It has been found that the SCN neurons differ in the amplitude relaxation rate, which represents the rigidity of the neurons to the external amplitude disturbance. Thus far, the appearance of that difference has not been explained. In the present study, an alternative explanation based on the Poincare′ model is given which takes into account the effect of the difference in the entrainment range of the SCN. Both our simulation results and theoretical analyses show that the largest entrainment range is obtained with suitable difference in the case that only a part of SCN neurons are sensitive to the light information. Our findings may give an alternative explanation for the appearance of that difference(heterogeneity) and shed light on the effects of the heterogeneity in the neuronal properties on the collective behaviors of the SCN neurons.展开更多
In this paper, we consider a class of reaction hyperbolic systems for axonal trans- port arising in neuroscience which can be regarded as hyperbolic systems with relaxation. We prove the BV entropy solutions of the hy...In this paper, we consider a class of reaction hyperbolic systems for axonal trans- port arising in neuroscience which can be regarded as hyperbolic systems with relaxation. We prove the BV entropy solutions of the hyperbolic systems converge toward to the unique entropy solution of the equilibrium equation at the optimal rate O（√δ） in L1 norm as the relaxation time δ tends to zero.展开更多
The rate of elapsed polymerization of polyhydroxyethylacrylate in gelatin has been studied to investigate the effect of co-monomers consumption at a given dose. The polymer gel dosimeters consisted of 2%～4% N,N-methy...The rate of elapsed polymerization of polyhydroxyethylacrylate in gelatin has been studied to investigate the effect of co-monomers consumption at a given dose. The polymer gel dosimeters consisted of 2%～4% N,N-methyelene-bis-acrylamide cross-linker,2%～4% 2-hydroxyethylacrylate monomer and gelatin at 3% and 5%. The dosimeters were irradiated by using 60Co teletherapy γ-ray source up to 20 Gy at a constant dose rate. The relaxation rate of water proton in the dosimeters at different doses and co-monomer concentrations were measured using a nuclear magnetic resonance spectroscopy. The rate of elapsed polymerization decreases with increasing the dose and the initial concentration of co-monomers. The rate of consumption of co-monomers increases with an increase of the polymerization and the gelatin content of the polymer gel.展开更多
基金The subject is supported by National Natural Sciences Foundation of China(10001036)
文摘This paper is concerned with the convergence rates to travelling waves for a relaxation model with general flux functions. Compared with former results in this direction, the main novelty in this paper lies in the fact that the initial disturbance can be chosen large in suitable norm. Our analysis is based on the L^1-stability results obtained by C. Mascia and R. Natalini in [12].
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11471185,11801030,and 11861131004)
文摘A relaxation-rate formula is presented for the entropic lattice Boltzmann model(ELBM) - a discrete kinetic theory for hydrodynamics. The simple formula not only guarantees the discrete time H-theorem but also gives full consideration to the consistency with hydrodynamics. The relaxation rate calculated with the formula effectively characterizes the drastic changes of the flow fields. By using this formula, the computational cost of the ELBM is significantly reduced and the model now can be efficiently used for a broad range of applications including high Reynolds number flows.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11875042,11505114,and 10975099)the Program for Professor of Special Appointment(Orientational Scholar)at Shanghai Institutions of Higher Learning,China(Grant Nos.QD2015016 and D-USST02)
文摘Adaption of circadian rhythms in behavioral and physiological activities to the external light–dark cycle is achieved through the main clock, i.e., the suprachiasmatic nucleus(SCN) of the brain in mammals. It has been found that the SCN neurons differ in the amplitude relaxation rate, which represents the rigidity of the neurons to the external amplitude disturbance. Thus far, the appearance of that difference has not been explained. In the present study, an alternative explanation based on the Poincare′ model is given which takes into account the effect of the difference in the entrainment range of the SCN. Both our simulation results and theoretical analyses show that the largest entrainment range is obtained with suitable difference in the case that only a part of SCN neurons are sensitive to the light information. Our findings may give an alternative explanation for the appearance of that difference(heterogeneity) and shed light on the effects of the heterogeneity in the neuronal properties on the collective behaviors of the SCN neurons.
基金partially supported by the NSFC(11371349)National Basic Research Program of China(973 Program)(2011CB808002)
文摘In this paper, we consider a class of reaction hyperbolic systems for axonal trans- port arising in neuroscience which can be regarded as hyperbolic systems with relaxation. We prove the BV entropy solutions of the hyperbolic systems converge toward to the unique entropy solution of the equilibrium equation at the optimal rate O（√δ） in L1 norm as the relaxation time δ tends to zero.
文摘The rate of elapsed polymerization of polyhydroxyethylacrylate in gelatin has been studied to investigate the effect of co-monomers consumption at a given dose. The polymer gel dosimeters consisted of 2%～4% N,N-methyelene-bis-acrylamide cross-linker,2%～4% 2-hydroxyethylacrylate monomer and gelatin at 3% and 5%. The dosimeters were irradiated by using 60Co teletherapy γ-ray source up to 20 Gy at a constant dose rate. The relaxation rate of water proton in the dosimeters at different doses and co-monomer concentrations were measured using a nuclear magnetic resonance spectroscopy. The rate of elapsed polymerization decreases with increasing the dose and the initial concentration of co-monomers. The rate of consumption of co-monomers increases with an increase of the polymerization and the gelatin content of the polymer gel.
