9,537 research outputs found
Spectral imbalance and the normalized dissipation rate of turbulence
The normalized turbulent dissipation rate is studied in decaying
and forced turbulence by direct numerical simulations, large-eddy simulations,
and closure calculations. A large difference in the values of is
observed for the two types of turbulence. This difference is found at moderate
Reynolds number, and it is shown that it persists at high Reynolds number,
where the value of becomes independent of the Reynolds number, but
is still not unique. This difference can be explained by the influence of the
nonlinear cascade time that introduces a spectral disequilibrium for
statistically nonstationary turbulence. Phenomenological analysis yields simple
analytical models that satisfactorily reproduce the numerical results. These
simple spectral models also reproduce and explain the increase of
at low Reynolds number that is observed in the simulations
Evidence for hard and soft substructures in thermoelectric SnSe
SnSe is a topical thermoelectric material with a low thermal conductivity
which is linked to its unique crystal structure. We use low-temperature heat
capacity measurements to demonstrate the presence of two characteristic
vibrational energy scales in SnSe with Debye temperatures thetaD1 = 345(9) K
and thetaD2 = 154(2) K. These hard and soft substructures are quantitatively
linked to the strong and weak Sn-Se bonds in the crystal structure. The heat
capacity model predicts the temperature evolution of the unit cell volume,
confirming that this two-substructure model captures the basic thermal
properties. Comparison with phonon calculations reveals that the soft
substructure is associated with the low energy phonon modes that are
responsible for the thermal transport. This suggests that searching for
materials containing highly divergent bond distances should be a fruitful route
for discovering low thermal conductivity materials.Comment: Accepted by Applied Physics Letter
Stability constants for some divalent metal ion/crown ether complexes in methanol determined by polarography and conductometry
Stability constants in methanol at 25.0°C were evaluated for the complexes of the divalent cations Ca2+, Ni2+, Zn2+, Pb2+, Mg2+, Co2+ and Cu2+ with the macrocyclic polyethers 15-crown-5 (15C5), 18-crown-6 (18C6), dicyclohexyl-18-crown-6 (DC18C6) and dibenzo-24-crown-8 (DB24C8). The log K values of the 1:1 complexes were generally in the range 2.1–4.2, which is low in comparison to the values of the corresponding crown ether/alkali metal ion complexes. M2L complexes were observed for the systems Pb2+/18C6, Pb2+/DC18C6, Ca2+/DC18C6 and Cu2+/D18C6, whereas ML2 complexes were found for Ca2+/18C6 and Cu2+/18C6. Within the series of complexes studied, there was no clear relationship between cation diameter and hole size
Equidistribution of the Fekete points on the sphere
The Fekete points are the points that maximize a Vandermonde-type determinant
that appears in the polynomial Lagrange interpolation formula. They are well
suited points for interpolation formulas and numerical integration. We prove
the asymptotic equidistribution of the Fekete points in the sphere. The way we
proceed is by showing their connection with other array of points, the
Marcinkiewicz-Zygmund arrays and the interpolating arrays, that have been
studied recently
A rescaled method for RBF approximation
A new method to compute stable kernel-based interpolants
has been presented by the second and third authors. This rescaled interpolation method combines the
standard kernel interpolation with a properly defined rescaling operation, which
smooths the oscillations of the interpolant. Although promising, this procedure
lacks a systematic theoretical investigation.
Through our analysis, this novel method can be understood as standard
kernel interpolation by means of a properly rescaled kernel. This point of view
allow us to consider its error and stability properties.
First, we prove that the method is an instance of the Shepard\u2019s method,
when certain weight functions are used. In particular, the method can reproduce
constant functions.
Second, it is possible to define a modified set of cardinal functions strictly
related to the ones of the not-rescaled kernel. Through these functions, we
define a Lebesgue function for the rescaled interpolation process, and study its
maximum - the Lebesgue constant - in different settings.
Also, a preliminary theoretical result on the estimation of the interpolation
error is presented.
As an application, we couple our method with a partition of unity algorithm.
This setting seems to be the most promising, and we illustrate its behavior with
some experiments
A rescaled method for RBF approximation
In the recent paper [8], a new method to compute stable kernel-based
interpolants has been presented. This \textit{rescaled interpolation} method
combines the standard kernel interpolation with a properly defined rescaling
operation, which smooths the oscillations of the interpolant. Although
promising, this procedure lacks a systematic theoretical investigation. Through
our analysis, this novel method can be understood as standard kernel
interpolation by means of a properly rescaled kernel. This point of view allow
us to consider its error and stability properties
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