103,203 research outputs found
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
Black Holes as Quantum Gravity Condensates
We model spherically symmetric black holes within the group field theory
formalism for quantum gravity via generalised condensate states, involving sums
over arbitrarily refined graphs (dual to 3d triangulations). The construction
relies heavily on both the combinatorial tools of random tensor models and the
quantum geometric data of loop quantum gravity, both part of the group field
theory formalism. Armed with the detailed microscopic structure, we compute the
entropy associated with the black hole horizon, which turns out to be
equivalently the Boltzmann entropy of its microscopic degrees of freedom and
the entanglement entropy between the inside and outside regions. We recover the
area law under very general conditions, as well as the Bekenstein-Hawking
formula. The result is also shown to be generically independent of any specific
value of the Immirzi parameter.Comment: 22 page
Semantic subtyping for objects and classes
In this paper we propose an integration of structural subtyping with boolean
connectives and semantic subtyping to define a Java-like programming language
that exploits the benefits of both techniques. Semantic subtyping is an approach
for defining subtyping relation based on set-theoretic models, rather than syntactic
rules. On the one hand, this approach involves some non trivial mathematical
machinery in the background. On the other hand, final users of the language need
not know this machinery and the resulting subtyping relation is very powerful and
intuitive. While semantic subtyping is naturally linked to the structural one, we
show how our framework can also accommodate the nominal subtyping. Several
examples show the expressivity and the practical advantages of our proposal
Fredholm factorization of Wiener-Hopf scalar and matrix kernels
A general theory to factorize the Wiener-Hopf (W-H) kernel using Fredholm Integral Equations (FIE) of the second kind is presented. This technique, hereafter called Fredholm factorization, factorizes the W-H kernel using simple numerical quadrature. W-H kernels can be either of scalar form or of matrix form with arbitrary dimensions. The kernel spectrum can be continuous (with branch points), discrete (with poles), or mixed (with branch points and poles). In order to validate the proposed method, rational matrix kernels in particular are studied since they admit exact closed form factorization. In the appendix a new analytical method to factorize rational matrix kernels is also described. The Fredholm factorization is discussed in detail, supplying several numerical tests. Physical aspects are also illustrated in the framework of scattering problems: in particular, diffraction problems. Mathematical proofs are reported in the pape
Locally preferred structures and many-body static correlations in viscous liquids
We investigate the influence of static correlations beyond the pair level on
the dynamics of selected model glass-formers. We compare the pair structure,
angular distribution functions, and statistics of Voronoi polyhedra of two
well-known Lennard-Jones mixtures as well as of the corresponding
Weeks-Chandler-Andersen variants, in which the attractive part of the potential
is truncated. By means of the Voronoi construction we identify the atomic
arrangements corresponding to the locally preferred structures of the models.
We find that the growth of domains formed by interconnected locally preferred
structures signals the onset of the slow dynamics regime and allows to
rationalize the different dynamic behaviors of the models. At low temperature,
the spatial extension of the structurally correlated domains, evaluated at
fixed relaxation time, increases with the fragility of the models and is
systematically reduced by truncating the attractions. In view of these results,
proper inclusion of many-body static correlations in theories of the glass
transition appears crucial for the description of the dynamics of fragile
glass-formers.Comment: 9 pages, 8 figures, added two tables, minor revisions to the tex
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