2,469 research outputs found
Regularity of the extremal solution for singular p-Laplace equations
We study the regularity of the extremal solution to the singular
reaction-diffusion problem in , on
, where , , is a smooth bounded domain and is any positive, superlinear,
increasing and (asymptotically) convex nonlinearity. We provide a simple
proof of known and \textit{a priori} estimates for , i.e.
if , if and if
Energetic model of tumor growth
A macroscopic model of the tumor Gompertzian growth is proposed. This
approach is based on the energetic balance among the different cell activities,
described by methods of statistical mechanics and related to the growth
inhibitor factors. The model is successfully applied to the multicellular tumor
spheroid data.Comment: 5 pages, 2 figures, contribution to "Complexity, Metastability and
Nonextensivity", Erice, July 200
Causality Constraints on Hadron Production In High Energy Collisions
For hadron production in high energy collisions, causality requirements lead
to the counterpart of the cosmological horizon problem: the production occurs
in a number of causally disconnected regions of finite space-time size. As a
result, globally conserved quantum numbers (charge, strangeness, baryon number)
must be conserved locally in spatially restricted correlation clusters. This
provides a theoretical basis for the observed suppression of strangeness
production in elementary interactions (pp, e^+e^-). In contrast, the space-time
superposition of many collisions in heavy ion interactions largely removes
these causality constraints, resulting in an ideal hadronic resonance gas in
full equilibrium.Comment: 16 pages,8 figure
Beyond the plane-parallel approximation for redshift surveys
Redshift space distortions privilege the location of the observer in
cosmological redshift surveys, breaking the translational symmetry of the
underlying theory. This violation of statistical homogeneity has consequences
for the modeling of clustering observables, leading to what are frequently
called `wide angle effects'. We study these effects analytically, computing
their signature in the clustering of the multipoles in configuration and
Fourier space. We take into account both physical wide angle contributions as
well as the terms generated by the galaxy selection function. Similar
considerations also affect the way power spectrum estimators are constructed.
We quantify, in an analytical way the biases which enter and clarify the
relation between what we measure and the underlying theoretical modeling. The
presence of an angular window function is also discussed. Motivated by this
analysis we present new estimators for the three dimensional Cartesian power
spectrum and bispectrum multipoles written in terms of spherical Fourier-Bessel
coefficients. We show how the latter have several interesting properties,
allowing in particular a clear separation between angular and radial modes.Comment: 16 pages, 5 figure
A global existence result for a Keller-Segel type system with supercritical initial data
We consider a parabolic-elliptic Keller-Segel type system, which is related
to a simplified model of chemotaxis. Concerning the maximal range of existence
of solutions, there are essentially two kinds of results: either global
existence in time for general subcritical () initial data,
or blow--up in finite time for suitably chosen supercritical
() initial data with concentration around finitely many
points. As a matter of fact there are no results claiming the existence of
global solutions in the supercritical case. We solve this problem here and
prove that, for a particular set of initial data which share large
supercritical masses, the corresponding solution is global and uniformly
bounded
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