1,964 research outputs found
Ternary and quaternary oxides of Bi, Sr, and Cu
Before the discovery of superconductivity in an oxide of Bi, Sr, and Cu, the system Bi-Sr-Cu-O had not been studied, although several solid phases had been identified in the two-component regions of the ternary system Bi2O3-SrO-CuO. The oxides Sr2CuO3, SrCu2O2, SrCuO2, and Bi2CuO4 were then well known and characterized, and the phase diagram of the binary system Bi2O3 -SrO had been established in the temperature range 620 to 1000 C. Besides nine solutions of compositions Bi(2-2x) Sr(x) O(3-2x) and different symmetries, this diagram includes three definite compounds of stoichiometries Bi(2)SrO4, Bi2Sr2O5, and Bi2Sr3O6 (x = 0.50, 0.67 and 0.75 respectively), only the second of which with known unit-cell of orthorhombic symmetry, dimensions (A) a = 14.293(2), b = 7.651(2), c = 6.172(1), and z = 4. The first superconducting oxide in the system Bi-Sr-Cu-O was initially formulated as Bi2Sr2Cu2O(7+x), with an orthorhombic unit-cell of parameters (A) a = 5.32, b = 26.6, c = 48.8. In a preliminary study the same oxide was formulated with half the copper content, Bi(2)Sr(2)CuO(6+x), and indexed its reflections assuming an orthorhombic unit-cell of dimensions (A) a = 5.390(2), b = 26.973(8), c = 24.69(4). Subsequent studies by diffraction techniques have confirmed the composition 2:2:1. A new family of oxygen-deficient perovskites, was characterized, after identifying by x ray diffraction the phases present in the products of thermal treatments of about 150 mixtures of analytical grade Bi2O3, Sr(OH)2-8H2O and CuO at different molar ratios. X ray diffraction data are presented for some other oxides of Bi and Sr, as well as for various quaternary oxides, among them an oxide of Bi, Sr, and Cu
Microcanonical Analysis of Exactness of the Mean-Field Theory in Long-Range Interacting Systems
Classical spin systems with nonadditive long-range interactions are studied
in the microcanonical ensemble. It is expected that the entropy of such a
system is identical to that of the corresponding mean-field model, which is
called "exactness of the mean-field theory". It is found out that this
expectation is not necessarily true if the microcanonical ensemble is not
equivalent to the canonical ensemble in the mean-field model. Moreover,
necessary and sufficient conditions for exactness of the mean-field theory are
obtained. These conditions are investigated for two concrete models, the
\alpha-Potts model with annealed vacancies and the \alpha-Potts model with
invisible states.Comment: 23 pages, to appear in J. Stat. Phy
Canonical Solution of Classical Magnetic Models with Long-Range Couplings
We study the canonical solution of a family of classical spin
models on a generic -dimensional lattice; the couplings between two spins
decay as the inverse of their distance raised to the power , with
. The control of the thermodynamic limit requires the introduction of
a rescaling factor in the potential energy, which makes the model extensive but
not additive. A detailed analysis of the asymptotic spectral properties of the
matrix of couplings was necessary to justify the saddle point method applied to
the integration of functions depending on a diverging number of variables. The
properties of a class of functions related to the modified Bessel functions had
to be investigated. For given , and for any , and lattice
geometry, the solution is equivalent to that of the model, where the
dimensionality and the geometry of the lattice are irrelevant.Comment: Submitted for publication in Journal of Statistical Physic
Exporting and capital investment: On the strategic behavior of exporters.
By exporting, firms sell in markets whose business cycles are not perfectly correlated, and so can be expected to have more stable cash flows. If companies are liquidity constrained, this stability of cash flows can provide exporters with certain advantages over firms that operate solely in a domestic market. For instance, under the existence of liquidity constraints, more stable cash flows should foster more stable capital investments. Moreover, the expectation of more stable future cash flows and the information signal from commencing exporting can lessen the severity of liquidity constraints for exporters compared to non-exporters. We test these arguments by examining a stratified representative sample of the Spanish manufacturing sector from 1990 to 1998. Our results suggest that exporters' cash flows and capital investments are more stable than non-exporters'. Moreover, we find that liquidity constraints are less binding for exporters than for non-exporters. The richness of our data allows us to examine alternative explanations for the results we present. We conclude by discussing the strategic implications of our findings for firms.Liquidity constraint; exporter; non-exporter
1-d gravity in infinite point distributions
The dynamics of infinite, asymptotically uniform, distributions of
self-gravitating particles in one spatial dimension provides a simple toy model
for the analogous three dimensional problem. We focus here on a limitation of
such models as treated so far in the literature: the force, as it has been
specified, is well defined in infinite point distributions only if there is a
centre of symmetry (i.e. the definition requires explicitly the breaking of
statistical translational invariance). The problem arises because naive
background subtraction (due to expansion, or by "Jeans' swindle" for the static
case), applied as in three dimensions, leaves an unregulated contribution to
the force due to surface mass fluctuations. Following a discussion by
Kiessling, we show that the problem may be resolved by defining the force in
infinite point distributions as the limit of an exponentially screened pair
interaction. We show that this prescription gives a well defined (finite) force
acting on particles in a class of perturbed infinite lattices, which are the
point processes relevant to cosmological N-body simulations. For identical
particles the dynamics of the simplest toy model is equivalent to that of an
infinite set of points with inverted harmonic oscillator potentials which
bounce elastically when they collide. We discuss previous results in the
literature, and present new results for the specific case of this simplest
(static) model starting from "shuffled lattice" initial conditions. These show
qualitative properties (notably its "self-similarity") of the evolution very
similar to those in the analogous simulations in three dimensions, which in
turn resemble those in the expanding universe.Comment: 20 pages, 8 figures, small changes (section II shortened, added
discussion in section IV), matches final version to appear in PR
Relaxation to thermal equilibrium in the self-gravitating sheet model
We revisit the issue of relaxation to thermal equilibrium in the so-called
"sheet model", i.e., particles in one dimension interacting by attractive
forces independent of their separation. We show that this relaxation may be
very clearly detected and characterized by following the evolution of order
parameters defined by appropriately normalized moments of the phase space
distribution which probe its entanglement in space and velocity coordinates.
For a class of quasi-stationary states which result from the violent relaxation
of rectangular waterbag initial conditions, characterized by their virial ratio
R_0, we show that relaxation occurs on a time scale which (i) scales
approximately linearly in the particle number N, and (ii) shows also a strong
dependence on R_0, with quasi-stationary states from colder initial conditions
relaxing much more rapidly. The temporal evolution of the order parameter may
be well described by a stretched exponential function. We study finally the
correlation of the relaxation times with the amplitude of fluctuations in the
relaxing quasi-stationary states, as well as the relation between temporal and
ensemble averages.Comment: 37 pages, 24 figures; some additional discussion of previous
literature and other minor modifications, final published versio
On the effectiveness of mixing in violent relaxation
Relaxation processes in collisionless dynamics lead to peculiar behavior in
systems with long-range interactions such as self-gravitating systems,
non-neutral plasmas and wave-particle systems. These systems, adequately
described by the Vlasov equation, present quasi-stationary states (QSS), i.e.
long lasting intermediate stages of the dynamics that occur after a short
significant evolution called "violent relaxation". The nature of the
relaxation, in the absence of collisions, is not yet fully understood. We
demonstrate in this article the occurrence of stretching and folding behavior
in numerical simulations of the Vlasov equation, providing a plausible
relaxation mechanism that brings the system from its initial condition into the
QSS regime. Area-preserving discrete-time maps with a mean-field coupling term
are found to display a similar behaviour in phase space as the Vlasov system.Comment: 10 pages, 11 figure
Linear theory and violent relaxation in long-range systems: a test case
In this article, several aspects of the dynamics of a toy model for longrange
Hamiltonian systems are tackled focusing on linearly unstable unmagnetized
(i.e. force-free) cold equilibria states of the Hamiltonian Mean Field (HMF).
For special cases, exact finite-N linear growth rates have been exhibited,
including, in some spatially inhomogeneous case, finite-N corrections. A random
matrix approach is then proposed to estimate the finite-N growth rate for some
random initial states. Within the continuous, , approach,
the growth rates are finally derived without restricting to spatially
homogeneous cases. All the numerical simulations show a very good agreement
with the different theoretical predictions. Then, these linear results are used
to discuss the large-time nonlinear evolution. A simple criterion is proposed
to measure the ability of the system to undergo a violent relaxation that
transports it in the vicinity of the equilibrium state within some linear
e-folding times
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