From the nonlinear Fokker-Planck equation to the Vlasov description and back: Confined interacting particles with drag

We investigate the dynamics of overdamped D-dimensional systems of particles repulsively interacting through short-ranged power-law potentials, V (r) ∼ r −λ (λ/D > 1). We show that such systems obey a non-linear diffusion equation, and that their stationary state extremizes a q-generalized nonadditive entropy. Here we focus on the dynamical evolution of these systems. Our first-principle D = 1, 2 many-body numerical simulations (based on Newton's law) confirm the predictions obtained from the time-dependent solution of the non-linear diffusion equation, and show that the one-particle space-distribution P (x, t) appears to follow a compact-support q-Gaussian form, with q = 1 − λ/D. We also calculate the velocity distributions P (vx, t) and, interestingly enough, they follow the same q-Gaussian form (apparently precisely for D = 1, and nearly so for D = 2). The satisfactory match between the continuum description and the molecular dynamics simulations in a more general, time-dependent, framework neatly confirms the idea that the present dissipative systems indeed represent suitable applications of the q-generalized thermostatistical theory.

show abstract

“…same form, namely, a q-Gaussian. This prediction is consistent with [23], and confirmed by the results of Fig. 3.…”

Section: Model Solutionsupporting

confidence: 89%

Overdamped dynamics of particles with repulsive power-law interactions

et al. 2018

View full text Add to dashboard Cite

show abstract

“…In addition, we obtain a correspondence between the stochastic differential equation and nonlinear Fokker-Planck equation obtained in the non-additive statistical mechanics different of the connection made in the literature. 24,25 .…”

Section: Discussionmentioning

confidence: 99%

“…Even though in literature has been used the Stratonovich equation to make the connection with the Fokker-Planck equation, 24 we have used here the Itô's stochastic differential equation (that is equivalent to a Stratonovich equation with additional term) to make the connection with the Fokker-Planck equation being hence, different from prescription usual.…”

Section: Existence and Uniquenessmentioning

confidence: 99%

Dynamics based on analysis of public data for spreading of disease

Lima

2021

Preprint

View full text Add to dashboard Cite

The stochastic model for epidemic spreading of the novel coronavirus disease based on the data set supported by the public health agencies in countries as Brazil, EUA and India is investigated. We perform the numerical analysis using the stochastic differential equation in Itô’s calculus (SDE) for the estimating of novel cases daily as well as analytical calculations solving the correspondent Fokker-Planck equation for the density probability distribution of novel cases, P(N(t); t). Our results display that the model based in the Itô diffusion fits well to the results due to uncertain in the official data and to the number of tests realized in the populations of each country.

show abstract

“…Even though in literature has been used the Stratonovich equation to make the connection with the Fokker–Planck equation 23 , we have used here the Itô’s stochastic differential equation (which is equivalent to a Stratonovich equation with an additional term) to make the connection with the Fokker–Planck equation being hence, different from prescription usually made.…”

Section: Nonlinear Fokker–planck Equationmentioning

confidence: 99%

Dynamics based on analysis of public data for spreading of disease

Lima

2021

Sci Rep

View full text Add to dashboard Cite

The stochastic model for epidemic spreading of the novel coronavirus disease based on the data set supply by the public health agencies in countries as Brazil, United States and India is investigated. We perform a numerical analysis using the stochastic differential equation in Itô’s calculus for the estimating of novel cases daily, as well as analytical calculations solving the correspondent Fokker–Planck equation for the probability density distribution of novel cases, P(N(t), t). Our results display that the model based in the Itô’s diffusion fits well to the results due to uncertainty in the official data and to the number of tests realized in populations of each country.

show abstract

From the nonlinear Fokker-Planck equation to the Vlasov description and back: Confined interacting particles with drag

Cited by 23 publications

References 57 publications

Overdamped dynamics of particles with repulsive power-law interactions

Overdamped dynamics of particles with repulsive power-law interactions

Dynamics based on analysis of public data for spreading of disease

Dynamics based on analysis of public data for spreading of disease

Contact Info

Product

Resources

About