1,806 research outputs found
Temperature-dependent Raman scattering of DyScO3 and GdScO3 single crystals
We report a temperature-dependent Raman scattering investigation of DyScO3
and GdScO3 single crystals from room temperature up to 1200 {\deg}C. With
increasing temperature, all modes decrease monotonously in wavenumber without
anomaly, which attests the absence of a structural phase transition. The high
temperature spectral signature and extrapolation of band positions to higher
temperatures suggest a decreasing orthorhombic distortion towards the ideal
cubic structure. Our study indicates that this orthorhombic-to-cubic phase
transition is close to or higher than the melting point of both rare-earth
scandates (\approx 2100 {\deg}C), which might exclude the possibility of the
experimental observation of such a phase transition before melting. The
temperature-dependent shift of Raman phonons is also discussed in the context
of thermal expansion
Comparing hierarchies of total functionals
In this paper we consider two hierarchies of hereditarily total and
continuous functionals over the reals based on one extensional and one
intensional representation of real numbers, and we discuss under which
asumptions these hierarchies coincide. This coincidense problem is equivalent
to a statement about the topology of the Kleene-Kreisel continuous functionals.
As a tool of independent interest, we show that the Kleene-Kreisel functionals
may be embedded into both these hierarchies.Comment: 28 page
An algorithmic approach to the existence of ideal objects in commutative algebra
The existence of ideal objects, such as maximal ideals in nonzero rings,
plays a crucial role in commutative algebra. These are typically justified
using Zorn's lemma, and thus pose a challenge from a computational point of
view. Giving a constructive meaning to ideal objects is a problem which dates
back to Hilbert's program, and today is still a central theme in the area of
dynamical algebra, which focuses on the elimination of ideal objects via
syntactic methods. In this paper, we take an alternative approach based on
Kreisel's no counterexample interpretation and sequential algorithms. We first
give a computational interpretation to an abstract maximality principle in the
countable setting via an intuitive, state based algorithm. We then carry out a
concrete case study, in which we give an algorithmic account of the result that
in any commutative ring, the intersection of all prime ideals is contained in
its nilradical
Existential witness extraction in classical realizability and via a negative translation
We show how to extract existential witnesses from classical proofs using
Krivine's classical realizability---where classical proofs are interpreted as
lambda-terms with the call/cc control operator. We first recall the basic
framework of classical realizability (in classical second-order arithmetic) and
show how to extend it with primitive numerals for faster computations. Then we
show how to perform witness extraction in this framework, by discussing several
techniques depending on the shape of the existential formula. In particular, we
show that in the Sigma01-case, Krivine's witness extraction method reduces to
Friedman's through a well-suited negative translation to intuitionistic
second-order arithmetic. Finally we discuss the advantages of using call/cc
rather than a negative translation, especially from the point of view of an
implementation.Comment: 52 pages. Accepted in Logical Methods for Computer Science (LMCS),
201
Infrared and THz studies of polar phonons and improper magnetodielectric effect in multiferroic BFO3 ceramics
BFO3 ceramics were investigated by means of infrared reflectivity and time
domain THz transmission spectroscopy at temperatures 20 - 950 K, and the
magnetodielectric effect was studied at 10 - 300 K, with the magnetic field up
to 9 T. Below 175 K, the sum of polar phonon contributions into the
permittivity corresponds to the value of measured permittivity below 1 MHz. At
higher temperatures, a giant low-frequency permittivity was observed, obviously
due to the enhanced conductivity and possible Maxwell-Wagner contribution.
Above 200 K the observed magnetodielectric effect is caused essentially through
the combination of magnetoresistance and the Maxwell-Wagner effect, as recently
predicted by Catalan (Appl. Phys. Lett. 88, 102902 (2006)). Since the
magnetodielectric effect does not occur due to a coupling of polarization and
magnetization as expected in magnetoferroelectrics, we call it improper
magnetodielectric effect. Below 175 K the magnetodielectric effect is by
several orders of magnitude lower due to the decreased conductivity. Several
phonons exhibit gradual softening with increasing temperature, which explains
the previously observed high-frequency permittivity increase on heating. The
observed non-complete phonon softening seems to be the consequence of the
first-order nature of the ferroelectric transition.Comment: subm. to PRB. revised version according to referees' report
On a class of invariant coframe operators with application to gravity
Let a differential 4D-manifold with a smooth coframe field be given. Consider
the operators on it that are linear in the second order derivatives or
quadratic in the first order derivatives of the coframe, both with coefficients
that depend on the coframe variables. The paper exhibits the class of operators
that are invariant under a general change of coordinates, and, also, invariant
under the global SO(1,3)-transformation of the coframe. A general class of
field equations is constructed. We display two subclasses in it. The subclass
of field equations that are derivable from action principles by free variations
and the subclass of field equations for which spherical-symmetric solutions,
Minkowskian at infinity exist. Then, for the spherical-symmetric solutions, the
resulting metric is computed. Invoking the Geodesic Postulate, we find all the
equations that are experimentally (by the 3 classical tests) indistinguishable
from Einstein field equations. This family includes, of course, also Einstein
equations. Moreover, it is shown, explicitly, how to exhibit it. The basic tool
employed in the paper is an invariant formulation reminiscent of Cartan's
structural equations. The article sheds light on the possibilities and
limitations of the coframe gravity. It may also serve as a general procedure to
derive covariant field equations
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