We consider Volterra integral equations on time scales and present our study about the long time behavior of their solutions. We provide sufficient conditions for the stability and investigate the convergence properties when the kernel of the equations vanishes at infinity.

Distributions of heavy particles suspended in incompressible turbulent flows are investigated by means of high-resolution direct numerical simulations. It is shown that particles form fractal clusters in the dissipative range, with properties independent of the Reynolds number. Conversely, in the inertial range, the particle distribution is not scale-invariant. It is however shown that deviations from uniformity depends only on a rescaled contraction rate, and not on the local Stokes number given by dimensional analysis.

The rheology and dynamics of suspensions of fluid vesicles is investigated by a combination of molecular dynamics and mesoscale hydrodynamics simulations in two dimensions. The vesicle suspension is confined between two no-slip shearing walls. The flow behavior is studied as a function of the shear rate, the volume fraction of vesicles, and the viscosity ratio between inside and outside fluids. Results are obtained for the interactions of two vesicles, the intrinsic viscosity of the suspension, and the cell-free layer near the walls.

Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 1950s with the Kierstead, Slobodkin, and Skellam (KiSS) model, namely a continuous reaction-diffusion equation for a population growing on a patch of finite size L surrounded by a deadly environment with infinite mortality, i.e., an oasis in a desert. The main outcome of the model is that only patches above a critical size allow for population persistence.

Background: Direct-acting antiviral drugs (DAA) regimen improve the SVR rate. However, adverse effects often lead to therapy interruption.

Broader comprehension of gene expression regulatory mechanisms can be gained from a global analysis of how transcription and degradation are coordinated to orchestrate complex cell responses. The role of messenger RNA (mRNA) turnover modulation in gene expression levels has become increasingly recognized.

We present results from recent direct numerical simulations of heavy particle transport in homogeneous, isotropic, fully developed turbulence, with grid resolution up to 5123 and R? ? 185. By following the trajectories of millions of particles with different Stokes numbers, St ? [0.16 : 3.5], we are able to characterize in full detail the statistics of particle acceleration. We focus on the probability density function of the normalised acceleration a/arms and on the behaviour of their rootmean-squared acceleration arms as a function of both St and R?.