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An analysis of the projectile motion in stagnant air is presented for an evaporating respiratory micro-droplet which has been ejected from the mouth as an isolated droplet. It is assumed that the air resistance is a nonlinear function of…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
We investigate the self-propulsion of an inertial active particle confined in a two-dimensional harmonic trap. The particle is suspended in a non-Newtonian or viscoelastic suspension with a friction kernel that decays exponentially with a…
When particles on a line collide, they may coalesce into one. Such systems arise in the voter model, where boundaries between opinion clusters perform coalescing random walks, and in reaction-diffusion theory, where diffusing particles…
Results presented in a recent paper "Which is the Quantum Decay Law of Relativistic particles?", arXiv: 1412.3346v2 [quant--ph]], are analyzed. We show that approximations used therein to derive the main final formula for the survival…
In this article, we study the stability in the inverse problem of determining the time-dependent convection term and density coefficient appearing in the convection-diffusion equation, from partial boundary measurements. For dimension…
We present a fully computable a posteriori error estimator for piecewise linear finite element approximations of reaction-diffusion problems with mixed boundary conditions and piecewise constant reaction coefficient formulated in arbitrary…
The effect of refractory periods in partial resetting processes is studied. Under Poissonian partial resets, a state variable jumps to a value closer to the origin by a fixed fraction at constant rate, $x\to a x$. Following each reset, a…
The phenomenon of Fermi acceleration is addressed for a dissipative bouncing ball model with external stochastic perturbation. It is shown that the introduction of energy dissipation (inelastic collisions of the particle with the moving…
We examine the stability of self-similar solutions for an accelerating relativistic blast wave which is generated by a point explosion in an external medium with a steep radial density profile of a power-law index > 4.134. These…
What are the mechanisms of particle acceleration and radiation, as well as magnetic field build up and decay in relativistic shocks are open questions with important implications to various phenomena in high energy astrophysics. While the…
Due to its ubiquitous presence, turbulence is often invoked to explain the origin of nonthermal particles in astrophysical sources of high-energy emission. With particle-in-cell simulations, we study decaying turbulence in…
In this work, we study continuity and topological structural stability of attractors for nonautonomous random differential equations obtained by small bounded random perturbations of autonomous semilinear problems. First, we study existence…
In this paper we consider the coalescence dynamics of a tagged particle moving in a random distribution of particles with volumes independently distributed according to a probability distribution (CTP model). We provide a rigorous…
The anomalous (i.e. non-Gaussian) dynamics of particles subject to a deterministic acceleration and a series of 'random kicks' is studied. Based on an extension of the concept of continuous time random walks to position-velocity space, a…
We present a quantum field theoretical derivation of the nondecay probability of an unstable particle with nonzero three-momentum $\mathbf{p}$. To this end, we use the (fully resummed) propagator of the unstable particle, denoted as $S,$ to…
We consider one dimensional random walks in random environment where every time the process stays at a location, it dies with a fixed probability. Under some mild assumptions it is easy to show that the survival probability goes to zero as…
Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…
We consider a jump-diffusion process on a bounded domain with reflection at the boundary, and establish long-term results for a general additive process of its path. This includes the long-term behaviour of its occupation time in the…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…