To sharpen the imaging of structures, it is vital to develop a convenient and efficient quantitative algorithm of the optical coherence tomography (OCT) sampling. In this paper a new Monte Carlo model is set up and ho...To sharpen the imaging of structures, it is vital to develop a convenient and efficient quantitative algorithm of the optical coherence tomography (OCT) sampling. In this paper a new Monte Carlo model is set up and how light propagates in bio-tissue is analyzed in virtue of mathematics and physics equations. The relations,in which light intensity of Class 1 and Class 2 light with different wavelengths changes with their permeation depth,and in which Class 1 light intensity (signal light intensity) changes with the probing depth, and in which angularly resolved diffuse reflectance and diffuse transmittance change with the exiting angle, are studied. The results show that Monte Carlo simulation results are consistent with the theory data.展开更多
Using 1200 CPUs of the National Supercomputer TH-A1 and a parallel integral algorithm based on the 3500th-order Taylor expansion and the 4180-digit multiple precision data,we have done a reliable simulation of chaotic...Using 1200 CPUs of the National Supercomputer TH-A1 and a parallel integral algorithm based on the 3500th-order Taylor expansion and the 4180-digit multiple precision data,we have done a reliable simulation of chaotic solution of Lorenz equation in a rather long interval 0 t 10000 LTU(Lorenz time unit).Such a kind of mathematically reliable chaotic simulation has never been reported.It provides us a numerical benchmark for mathematically reliable long-term prediction of chaos.Besides,it also proposes a safe method for mathematically reliable simulations of chaos in a finite but long enough interval.In addition,our very fine simulations suggest that such a kind of mathematically reliable long-term prediction of chaotic solution might have no physical meanings,because the inherent physical micro-level uncertainty due to thermal fluctuation might quickly transfer into macroscopic uncertainty so that trajectories for a long enough time would be essentially uncertain in physics.展开更多
In this paper, a novel method for linearization of rational second order nonlinear models is discussed. In particular, we discuss an application of the 5 expansion method （created to deal with problems in Quantum Fie...In this paper, a novel method for linearization of rational second order nonlinear models is discussed. In particular, we discuss an application of the 5 expansion method （created to deal with problems in Quantum Field Theory） which will enable both the linearization and perturbation expansion of such equations. Such a method allows for one to quickly obtain the order zero perturbation theory in terms of certain special functions which are governed by linear equations. Higher order perturbation theories can then be obtained in terms of such special functions. One benefit to such a method is that it may be applied even to models without small physical parameters, as the perturbation is given in terms of the degree of nonlinearity, rather than any physical parameter. As an application, we discuss a method of linearizing the six Painlev~ equations by an application of the method. In addition to highlighting the benefits of the method, we discuss certain shortcomings of the method.展开更多
In this paper, we present a method for constructing a Dulac function for mathematical models in population biology, in the form of systems of ordinary differential equations in the plane.
文摘To sharpen the imaging of structures, it is vital to develop a convenient and efficient quantitative algorithm of the optical coherence tomography (OCT) sampling. In this paper a new Monte Carlo model is set up and how light propagates in bio-tissue is analyzed in virtue of mathematics and physics equations. The relations,in which light intensity of Class 1 and Class 2 light with different wavelengths changes with their permeation depth,and in which Class 1 light intensity (signal light intensity) changes with the probing depth, and in which angularly resolved diffuse reflectance and diffuse transmittance change with the exiting angle, are studied. The results show that Monte Carlo simulation results are consistent with the theory data.
基金partly supported by National Natural Science Foundation of China (Grant No. 11272209)National Basic Research Program of China (Grant No. 2011CB309704)State Key Laboratory of Ocean Engineering of China (Grant No. GKZD010056).
文摘Using 1200 CPUs of the National Supercomputer TH-A1 and a parallel integral algorithm based on the 3500th-order Taylor expansion and the 4180-digit multiple precision data,we have done a reliable simulation of chaotic solution of Lorenz equation in a rather long interval 0 t 10000 LTU(Lorenz time unit).Such a kind of mathematically reliable chaotic simulation has never been reported.It provides us a numerical benchmark for mathematically reliable long-term prediction of chaos.Besides,it also proposes a safe method for mathematically reliable simulations of chaos in a finite but long enough interval.In addition,our very fine simulations suggest that such a kind of mathematically reliable long-term prediction of chaotic solution might have no physical meanings,because the inherent physical micro-level uncertainty due to thermal fluctuation might quickly transfer into macroscopic uncertainty so that trajectories for a long enough time would be essentially uncertain in physics.
文摘In this paper, a novel method for linearization of rational second order nonlinear models is discussed. In particular, we discuss an application of the 5 expansion method （created to deal with problems in Quantum Field Theory） which will enable both the linearization and perturbation expansion of such equations. Such a method allows for one to quickly obtain the order zero perturbation theory in terms of certain special functions which are governed by linear equations. Higher order perturbation theories can then be obtained in terms of such special functions. One benefit to such a method is that it may be applied even to models without small physical parameters, as the perturbation is given in terms of the degree of nonlinearity, rather than any physical parameter. As an application, we discuss a method of linearizing the six Painlev~ equations by an application of the method. In addition to highlighting the benefits of the method, we discuss certain shortcomings of the method.
文摘In this paper, we present a method for constructing a Dulac function for mathematical models in population biology, in the form of systems of ordinary differential equations in the plane.
