相关论文: Slowing Allee effect vs. accelerating heavy tails …
We study the formation and the evolution of velocity distribution tails for systems with long-range interactions. In the thermal bath approximation, the evolution of the distribution function of a test particle is governed by a…
In optical non-linear processes rogue waves can be observed, which can be mathematically described by heavy-tailed distributions. These distributions are special due to the fact that the probability of registering extremely high intensities…
We study the empirical version of halfspace depths with the objective of establishing a connection between the rates of convergence and the tail behaviour of the corresponding underlying distributions. The intricate interplay between the…
Complete and physically adequate analytical and semi-analytical solutions have been obtained using a practical dimensionless form of kinetic equation assuming azimuthal symmetry and Maxwellian distributions of target plasma species.…
We derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered \alpha-stable processes. Its most important application is to overcome the infinite-moment difficulty for the \alpha-stable random…
We investigate a class of parametric elliptic semilinear partial differential equations of second order with homogeneous essential boundary conditions, where the coefficients and the right-hand side (and hence the solution) may depend on a…
To rigorously model fast ions in fusion plasmas, a non-Maxwellian equilibrium distribution must be used. In the work, the response of high-energy alpha particles to electrostatic turbulence has been analyzed for several different tokamak…
This article illustrates how very small deviations from the Maxwellian exponential tail, while leaving unchanged bulk quantities, can yield dramatic effects on fusion reaction rates and discuss several mechanisms that can cause such…
An Allee effect occurs when the per-capita growth rate increases at low densities. Here, we investigate the evolutionary stability of a partial migration population with migrant population experiencing Allee effects. Partial migration is a…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
We derive sufficient conditions for the existence of a periodic traveling wave solution to an integro-difference equation with a piecewise constant growth function exhibiting a stable period2 cycle and strong Allee effect. The mean…
We present in this document the Lebesgue and Sobolev propagation of exponential tails for solutions of the homogeneous Boltzmann equation for hard and Maxwell interactions. In addition, we show the $L^{p}$-integrability creation of such…
In this paper, we study the large time behaviour of solutions of multistable reaction-diffusion equations in $\mathbb{R}^N$, with a spatially periodic heterogeneity. By multistable, we mean that the problem admits a finite -- but…
We consider stochastic processes where randomly chosen particles with positive quantities x, y (> 0) interact and exchange the quantities asymmetrically by the rule x' = c{(1-a) x + b y}, y' = d{a x + (1-b) y} (x \ge y), where (0 \le) a, b…
Discontinuous transitions into absorbing states require an effective mechanism that prevents the stabilization of low density states. They can be found in different systems, such as lattice models or stochastic differential equations (e.g.…
The Lagrangian velocity statistics of dissipative drift-wave turbulence are investigated. For large values of the adiabaticity (or small collisionality), the probability density function of the Lagrangian acceleration shows exponential…
Nonlinear effects in emission and absorption spectra of gaseous systems are considered. It is shown that level splitting can be detected spectroscopically even if it is below the Doppler width. Conditions for distinguishing interference…
Mass-conserving reaction-diffusion systems with bistable nonlinearity are considered under general assumptions. The existence of stationary solutions with a single internal transition layer in such reaction-diffusion systems is shown using…
We solve the quasiclassical problem of tunneling through an external potential barrier in a dense plasma, where the tunneling particles undergo simultaneous collisions with other particles in thermodynamic equilibrium. Under such conditions…
Strong anomalous diffusion is {often} characterized by a piecewise-linear spectrum of the moments of displacement. The spectrum is characterized by slopes $\xi$ and $\zeta$ for small and large moments, respectively, and by the critical…