Two new solutions of the homogeneous diffusion equation in 1D are derived in the presence of losses and a trigonometric profile for a profile of density. A simulation for the ankle in the energy distribution of cosmic...Two new solutions of the homogeneous diffusion equation in 1D are derived in the presence of losses and a trigonometric profile for a profile of density. A simulation for the ankle in the energy distribution of cosmic rays (CRs) is provided in the framework of the fine tuning of the involved parameters. A theoretical image for the overall diffusion of CRs in galactic coordinates is provided.展开更多
In recent years,the epidemic model with anomalous diffusion has gained popularity in the literature.However,when introducing anomalous diffusion into epidemic models,they frequently lack physical explanation,in contra...In recent years,the epidemic model with anomalous diffusion has gained popularity in the literature.However,when introducing anomalous diffusion into epidemic models,they frequently lack physical explanation,in contrast to the traditional reaction-diffusion epidemic models.The point of this paper is to guarantee that anomalous diffusion systems on infectious disease spreading remain physically reasonable.Specifically,based on the continuous-time random walk(CTRW),starting from two stochastic processes of the waiting time and the step length,time-fractional space-fractional diffusion,timefractional reaction-diffusion and fractional-order diffusion can all be naturally introduced into the SIR(S:susceptible,I:infectious and R:recovered)epidemic models,respectively.The three models mentioned above can also be applied to create SIR epidemic models with generalized distributed time delays.Distributed time delay systems can also be reduced to existing models,such as the standard SIR model,the fractional infectivity model and others,within the proper bounds.Meanwhile,as an application of the above stochastic modeling method,the physical meaning of anomalous diffusion is also considered by taking the SEIR(E:exposed)epidemic model as an example.Similar methods can be used to build other types of epidemic models,including SIVRS(V:vaccine),SIQRS(Q:quarantined)and others.Finally,this paper describes the transmission of infectious disease in space using the real data of COVID-19.展开更多
The anomalous redshift on the sun’s limb and that measured by Pioneer-6 are interesting for the process of absorption of light and the spatial density of matter around the sun. Here we derive a 3D solution for the di...The anomalous redshift on the sun’s limb and that measured by Pioneer-6 are interesting for the process of absorption of light and the spatial density of matter around the sun. Here we derive a 3D solution for the diffusion equation in the case of the steady state, which is then adopted as the density of the ionized matter around the sun. In order to deal with the observed light’s intensity, two integrals along the line of sight are evaluated. Alternatives to the Doppler shift have been considered as mechanisms: a thermal model, a plasma effect, the interaction of a low density electromagnetic wave with an electron and the interaction of light with a low density Fermi gas in standard QED. These four models are compared in the case of the Pioneer-6 signal.展开更多
We studied the foraging processes of wildebeest using an advection-diffusion equation. We equipped the model with data collected between 1999 and 2007 from the Serengeti ecosystem from 18 GPS-collared wildebeest. Resu...We studied the foraging processes of wildebeest using an advection-diffusion equation. We equipped the model with data collected between 1999 and 2007 from the Serengeti ecosystem from 18 GPS-collared wildebeest. Results analysis show that wildebeest foraging behavior can be explained by advective and diffusive parameters in a heterogeneous habitat like the Serengeti ecosystem.展开更多
Recent developments in the measurement of radioactive gases in passive diffusion motivate the analysis of Brownian motion of decaying particles, a subject that has received little previous attention. This paper report...Recent developments in the measurement of radioactive gases in passive diffusion motivate the analysis of Brownian motion of decaying particles, a subject that has received little previous attention. This paper reports the derivation and solution of equations comparable to the Fokker-Planck and Langevin equations for one-dimensional diffusion and decay of unstable particles. In marked contrast to the case of stable particles, the two equations are not equivalent, but provide different information regarding the same stochastic process. The differences arise because Brownian motion with particle decay is not a continuous process. The discontinuity is readily apparent in the computer-simulated trajectories of the Langevin equation that incorporate both a Wiener process for displacement fluctuations and a Bernoulli process for random decay. This paper also reports the derivation of the mean time of first passage of the decaying particle to absorbing boundaries. Here, too, particle decay can lead to an outcome markedly different from that for stable particles. In particular, the first-passage time of the decaying particle is always finite, whereas the time for a stable particle to reach a single absorbing boundary is theoretically infinite due to the heavy tail of the inverse Gaussian density. The methodology developed in this paper should prove useful in the investigation of radioactive gases, aerosols of radioactive atoms, dust particles to which adhere radioactive ions, as well as diffusing gases and liquids of unstable molecules.展开更多
文摘Two new solutions of the homogeneous diffusion equation in 1D are derived in the presence of losses and a trigonometric profile for a profile of density. A simulation for the ankle in the energy distribution of cosmic rays (CRs) is provided in the framework of the fine tuning of the involved parameters. A theoretical image for the overall diffusion of CRs in galactic coordinates is provided.
基金This work is supported in part by the National Natural Science Foundation of China(Grant Nos.62173027,62003026 and 61973329)the Natural Science Foundation of Beijing Municipality(Grant No.Z180005)Alianza UCMX seed funding(2020-2022)on Binational Collaborative Projects addressing COVID-19.
文摘In recent years,the epidemic model with anomalous diffusion has gained popularity in the literature.However,when introducing anomalous diffusion into epidemic models,they frequently lack physical explanation,in contrast to the traditional reaction-diffusion epidemic models.The point of this paper is to guarantee that anomalous diffusion systems on infectious disease spreading remain physically reasonable.Specifically,based on the continuous-time random walk(CTRW),starting from two stochastic processes of the waiting time and the step length,time-fractional space-fractional diffusion,timefractional reaction-diffusion and fractional-order diffusion can all be naturally introduced into the SIR(S:susceptible,I:infectious and R:recovered)epidemic models,respectively.The three models mentioned above can also be applied to create SIR epidemic models with generalized distributed time delays.Distributed time delay systems can also be reduced to existing models,such as the standard SIR model,the fractional infectivity model and others,within the proper bounds.Meanwhile,as an application of the above stochastic modeling method,the physical meaning of anomalous diffusion is also considered by taking the SEIR(E:exposed)epidemic model as an example.Similar methods can be used to build other types of epidemic models,including SIVRS(V:vaccine),SIQRS(Q:quarantined)and others.Finally,this paper describes the transmission of infectious disease in space using the real data of COVID-19.
文摘The anomalous redshift on the sun’s limb and that measured by Pioneer-6 are interesting for the process of absorption of light and the spatial density of matter around the sun. Here we derive a 3D solution for the diffusion equation in the case of the steady state, which is then adopted as the density of the ionized matter around the sun. In order to deal with the observed light’s intensity, two integrals along the line of sight are evaluated. Alternatives to the Doppler shift have been considered as mechanisms: a thermal model, a plasma effect, the interaction of a low density electromagnetic wave with an electron and the interaction of light with a low density Fermi gas in standard QED. These four models are compared in the case of the Pioneer-6 signal.
文摘We studied the foraging processes of wildebeest using an advection-diffusion equation. We equipped the model with data collected between 1999 and 2007 from the Serengeti ecosystem from 18 GPS-collared wildebeest. Results analysis show that wildebeest foraging behavior can be explained by advective and diffusive parameters in a heterogeneous habitat like the Serengeti ecosystem.
文摘Recent developments in the measurement of radioactive gases in passive diffusion motivate the analysis of Brownian motion of decaying particles, a subject that has received little previous attention. This paper reports the derivation and solution of equations comparable to the Fokker-Planck and Langevin equations for one-dimensional diffusion and decay of unstable particles. In marked contrast to the case of stable particles, the two equations are not equivalent, but provide different information regarding the same stochastic process. The differences arise because Brownian motion with particle decay is not a continuous process. The discontinuity is readily apparent in the computer-simulated trajectories of the Langevin equation that incorporate both a Wiener process for displacement fluctuations and a Bernoulli process for random decay. This paper also reports the derivation of the mean time of first passage of the decaying particle to absorbing boundaries. Here, too, particle decay can lead to an outcome markedly different from that for stable particles. In particular, the first-passage time of the decaying particle is always finite, whereas the time for a stable particle to reach a single absorbing boundary is theoretically infinite due to the heavy tail of the inverse Gaussian density. The methodology developed in this paper should prove useful in the investigation of radioactive gases, aerosols of radioactive atoms, dust particles to which adhere radioactive ions, as well as diffusing gases and liquids of unstable molecules.
