9,278 research outputs found
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 (with the number density and 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
and the melting at . 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
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