10,775 research outputs found
Elliptic regularity theory applied to time harmonic anisotropic Maxwell's equations with less than Lipschitz complex coefficients
The focus of this paper is the study of the regularity properties of the time
harmonic Maxwell's equations with anisotropic complex coefficients, in a
bounded domain with boundary. We assume that at least one of the
material parameters is for some . Using regularity
theory for second order elliptic partial differential equations, we derive
estimates and H\"older estimates for electric and magnetic fields up
to the boundary. We also derive interior estimates in bi-anisotropic media.Comment: 19 page
Quasi exactly solvable matrix Schroedinger operators
Two families of quasi exactly solvable 2*2 matrix Schroedinger operators are
constructed. The first one is based on a polynomial matrix potential and
depends on three parameters. The second is a one-parameter generalisation of
the scalar Lame equation. The relationship between these operators and QES
Hamiltonians already considered in the literature is pointed out.Comment: LaTeX, 9 pp, new results adde
Q-ball formation at the deconfinement temperature in large- QCD
The deconfinement phase transition in large- QCD is studied within the
framework of an effective Polyakov-loop model, where the potential has a U(1)
symmetry originating in the large- limit of a Z-symmetric model.
At the critical temperature, the shape of the effective potential allows the
existence of Q-balls as position-dependent fluctuations of the Polyakov loop.
Q-balls with spherical or axial symmetry are numerically obtained from the
equations of motion of the effective model under consideration. The physical
properties of these non-topological solitons (mass, charge and size) are
discussed, as well as their interpretation in terms of spinning "bubbles", with
various shapes, of deconfined matter surrounded by a confined environment.Comment: 21 pages, 8 figures ; v2 matches the published versio
Event-plane correlators
Correlators between event planes of different harmonics in relativistic
heavy-ion collisions have the potential to provide crucial information on the
initial state of the matter formed in these collisions. We present a new
procedure for analyzing such correlators, which is less demanding in terms of
detector acceptance than the one used recently by the ATLAS collaboration to
measure various two-plane and three-plane correlators in Pb-Pb collisions at
LHC. It can also be used unambiguously for quantitative comparison between
theory and data. We use this procedure to carry out realistic simulations
within the transport model AMPT. Our theoretical results are in excellent
agreement with the ATLAS data, in contrast with previous hydrodynamic
calculations which only achieved qualitative agreement. We present predictions
for new correlators, in particular four-plane correlators, which can easily be
analyzed with our new method.Comment: 6 pages, 3 figures. v2: Further explanations added; results unchange
Threshold effects In multivariate error correction models
In this paper we propose a testing procedure for assessing the presence of threshold effects in nonstationary Vector autoregressive models with or without cointegration. Our approach involves first testing whether the long run impact matrix characterising the VECM type representation of the VAR switches according to the magnitude of some threshold variable and is valid regardless of whether the system is purely I(1), I(1) with cointegration or stationary. Once the potential presence of threshold effects is established we subsequently evaluate the cointegrating properties of the system in each regime through a model selection based approach whose asymptotic and finite sample properties are also established. This subsequently allows us to introduce a novel non-linear permanent and transitory decomposition of the vector process of interest.
Angularly excited and interacting boson stars and Q-balls
We study angularly excited as well as interacting non-topological solitons,
so-called Q-balls and their gravitating counterparts, so-called boson stars in
3+1 dimensions. Q-balls and boson stars carry a non-vanishing Noether charge
and arise as solutions of complex scalar field models in a flat space-time
background and coupled minimally to gravity, respectively.
We present examples of interacting Q-balls that arise due to angular
excitations, which are closely related to the spherical harmonics. We also
construct explicit examples of rotating boson stars that interact with
non-rotating boson stars. We observe that rotating boson stars tend to absorb
the non-rotating ones for increasing, but reasonably small gravitational
coupling. This is a new phenomenon as compared to the flat space-time limit and
is related to the negative contribution of the rotation term to the energy
density of the solutions. In addition, our results indicate that a system of a
rotating and non-rotating boson star can become unstable if the direct
interaction term in the potential is large enough. This instability is related
to the appearance of ergoregions.Comment: 20 pages including 9 figures; for higher quality figures please
contact the authors; v2: minor changes, final version to appear in Phys. Rev.
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