Generalized transition fronts for one-dimensional almost periodic Fisher-KPP equations

This paper investigates the existence of generalized transition fronts for Fisher-KPP equations in one-dimensional, almost periodic media. Assuming that the linearized elliptic operator near the unstable steady state admits an almost periodic eigenfunction, we show that such fronts exist if and only if their average speed is above an explicit threshold. This hypothesis is satisfied in particular when the reaction term does not depend on x or (in some cases) is small enough. Moreover, except for the threshold case, the fronts we construct and their speeds are almost periodic, in a sense. When our hypothesis is no longer satisfied, such generalized transition fronts still exist for an interval of average speeds, with explicit bounds. Our proof relies on the construction of sub and super solutions based on an accurate analysis of the properties of the generalized principal eigenvalues

Path-Integral Ground-State and Superfluid Hydrodynamics of a Bosonic Gas of Hard Spheres

We study a bosonic gas of hard spheres by using of the exact zero-temperature Path-Integral Ground-State (PIGS) Monte Carlo method and the equations of superfluid hydrodynamics. The PIGS method is implemented to calculate for the bulk system the energy per particle and the condensate fraction through a large range of the gas parameter $na^3$ (with $n$ the number density and $a$ the s--wave scattering length), going from the dilute gas into the solid phase. The Maxwell construction is then adopted to determine the freezing at $na^3=0.278\pm 0.001$ and the melting at $na^3=0.286\pm 0.001$. In the liquid phase, where the condensate fraction is finite, the equations of superfluid hydrodynamics, based on the PIGS equation of state, are used to find other relevant quantities as a function of the gas parameter: the chemical potential, the pressure and the sound velocity. In addition, within the Feynman's approximation, from the PIGS static structure factor we determine the full excitation spectrum, which displays a maxon-roton behavior when the gas parameter is close to the freezing value. Finally, the equations of superfluid hydrodynamics with the PIGS equation of state are solved for bosonic system under axially--symmetric harmonic confinement obtaining its collective breathing modes.Comment: 7 pages, 7 figures; improved version to be published in Phys. Rev.

The Impact of Projection and Backboning on Network Topologies

Bipartite networks are a well known strategy to study a variety of phenomena. The commonly used method to deal with this type of network is to project the bipartite data into a unipartite weighted graph and then using a backboning technique to extract only the meaningful edges. Despite the wide availability of different methods both for projection and backboning, we believe that there has been little attention to the effect that the combination of these two processes has on the data and on the resulting network topology. In this paper we study the effect that the possible combinations of projection and backboning techniques have on a bipartite network. We show that the 12 methods group into two clusters producing unipartite networks with very different topologies. We also show that the resulting level of network centralization is highly affected by the combination of projection and backboning applied