81,774 research outputs found
Positive approximations of the inverse of fractional powers of SPD M-matrices
This study is motivated by the recent development in the fractional calculus
and its applications. During last few years, several different techniques are
proposed to localize the nonlocal fractional diffusion operator. They are based
on transformation of the original problem to a local elliptic or
pseudoparabolic problem, or to an integral representation of the solution, thus
increasing the dimension of the computational domain. More recently, an
alternative approach aimed at reducing the computational complexity was
developed. The linear algebraic system , is considered, where is a properly normalized (scalded) symmetric
and positive definite matrix obtained from finite element or finite difference
approximation of second order elliptic problems in ,
. The method is based on best uniform rational approximations (BURA)
of the function for and natural .
The maximum principles are among the major qualitative properties of linear
elliptic operators/PDEs. In many studies and applications, it is important that
such properties are preserved by the selected numerical solution method. In
this paper we present and analyze the properties of positive approximations of
obtained by the BURA technique. Sufficient conditions for
positiveness are proven, complemented by sharp error estimates. The theoretical
results are supported by representative numerical tests
QCD Sum Rules and Applications to Nuclear Physics
Applications of QCD sum-rule methods to the physics of nuclei are reviewed,
with an emphasis on calculations of baryon self-energies in infinite nuclear
matter. The sum-rule approach relates spectral properties of hadrons
propagating in the finite-density medium, such as optical potentials for
quasinucleons, to matrix elements of QCD composite operators (condensates). The
vacuum formalism for QCD sum rules is generalized to finite density, and the
strategy and implementation of the approach is discussed. Predictions for
baryon self-energies are compared to those suggested by relativistic nuclear
physics phenomenology. Sum rules for vector mesons in dense nuclear matter are
also considered.Comment: 92 pages, ReVTeX, 9 figures can be obtained upon request (to Xuemin
Jin
Degenerate Stars and Gravitational Collapse in AdS/CFT
We construct composite CFT operators from a large number of fermionic primary
fields corresponding to states that are holographically dual to a zero
temperature Fermi gas in AdS space. We identify a large N regime in which the
fermions behave as free particles. In the hydrodynamic limit the Fermi gas
forms a degenerate star with a radius determined by the Fermi level, and a mass
and angular momentum that exactly matches the boundary calculations. Next we
consider an interacting regime, and calculate the effect of the gravitational
back-reaction on the radius and the mass of the star using the
Tolman-Oppenheimer-Volkoff equations. Ignoring other interactions, we determine
the "Chandrasekhar limit" beyond which the degenerate star (presumably)
undergoes gravitational collapse towards a black hole. This is interpreted on
the boundary as a high density phase transition from a cold baryonic phase to a
hot deconfined phase.Comment: 75 page
Magnons in the ferromagnetic Kondo-lattice model
The magnetic properties of the ferromagnetic Kondo-lattice model (FKLM) are
investigated. Starting from an analysis of the magnon spectrum in the spin-wave
regime, we examine the ferromagnetic stability as a function of the occupation
of the conduction band and the strength of the coupling between the
localised moments and the conduction electrons. From the properties of the
spin-wave stiffness the ferromagnetic phase at zero temperature is derived.
Using an approximate formula the critical temperature is calculated as a
function of and .Comment: 15 pages, 6 figures, to appear in phys. stat. sol.
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