6,029 research outputs found
Reynolds number effect on the velocity increment skewness in isotropic turbulence
Second and third order longitudinal structure functions and wavenumber
spectra of isotropic turbulence are computed using the EDQNM model and compared
to results of the multifractal formalism. At the highest Reynolds number
available in windtunnel experiments, , both the multifractal
model and EDQNM give power-law corrections to the inertial range scaling of the
velocity increment skewness. For EDQNM, this correction is a finite Reynolds
number effect, whereas for the multifractal formalism it is an intermittency
correction that persists at any high Reynolds number. Furthermore, the two
approaches yield realistic behavior of second and third order statistics of the
velocity fluctuations in the dissipative and near-dissipative ranges.
Similarities and differences are highlighted, in particular the Reynolds number
dependence
Sliding friction between an elastomer network and a grafted polymer layer: the role of cooperative effects
We study the friction between a flat solid surface where polymer chains have
been end-grafted and a cross-linked elastomer at low sliding velocity. The
contribution of isolated grafted chains' penetration in the sliding elastomer
has been early identified as a weakly velocity dependent pull-out force. Recent
experiments have shown that the interactions between the grafted chains at high
grafting density modify the friction force by grafted chain. We develop here a
simple model that takes into account those interactions and gives a limit
grafting density beyond which the friction no longer increases with the
grafting density, in good agreement with the experimental dataComment: Submitted to Europhys. Letter
On the unsteady behavior of turbulence models
Periodically forced turbulence is used as a test case to evaluate the
predictions of two-equation and multiple-scale turbulence models in unsteady
flows. The limitations of the two-equation model are shown to originate in the
basic assumption of spectral equilibrium. A multiple-scale model based on a
picture of stepwise energy cascade overcomes some of these limitations, but the
absence of nonlocal interactions proves to lead to poor predictions of the time
variation of the dissipation rate. A new multiple-scale model that includes
nonlocal interactions is proposed and shown to reproduce the main features of
the frequency response correctly
Reassessment of the classical closures for scalar turbulence
In deducing the consequences of the Direct Interaction Approximation, Kraichnan was sometimes led to consider the properties of special classes of nonlinear interactions in degenerate triads in which one wavevector is very small. Such interactions can be described by simplified models closely related to elementary closures for homogeneous isotropic turbulence such as the Heisenberg and Leith models. These connections can be exploited to derive considerably improved versions of the Heisenberg and Leith models that are only slightly more complicated analytically. This paper applies this approach to derive some new simplified closure models for passive scalar advection and investigates the consistency of these models with fundamental properties of scalar turbulence. Whereas some properties, such as the existence of the KolmogorovâObukhov range and the existence of thermal equilibrium ensembles, follow the velocity case closely, phenomena special to the scalar case arise when the diffusive and viscous effects become important at different scales of motion. These include the Batchelor and Batchelorâ HowellsâTownsend ranges pertaining, respectively, to high and low molecular Schmidt number. We also consider the spectrum in the diffusive range that follows the Batchelor range. We conclude that improved elementary models can be made consistent with many nontrivial properties of scalar turbulence, but that such models have unavoidable limitations
Random Time Forward Starting Options
We introduce a natural generalization of the forward-starting options, first
discussed by M. Rubinstein. The main feature of the contract presented here is
that the strike-determination time is not fixed ex-ante, but allowed to be
random, usually related to the occurrence of some event, either of financial
nature or not. We will call these options {\bf Random Time Forward Starting
(RTFS)}. We show that, under an appropriate "martingale preserving" hypothesis,
we can exhibit arbitrage free prices, which can be explicitly computed in many
classical market models, at least under independence between the random time
and the assets' prices. Practical implementations of the pricing methodologies
are also provided. Finally a credit value adjustment formula for these OTC
options is computed for the unilateral counterparty credit risk.Comment: 19 pages, 1 figur
Small Scale Response and Modeling of Periodically Forced Turbulence
The response of the small scales of isotropic turbulence to periodic large scale forcing is studied using two-point closures. The frequency response of the turbulent kinetic energy and dissipation rate, and the phase shifts between production, energy and dissipation are determined as functions of Reynolds number. It is observed that the amplitude and phase of the dissipation exhibit nontrivial frequency and Reynolds number dependence that reveals a filtering effect of the energy cascade. Perturbation analysis is applied to understand this behavior which is shown to depend on distant interactions between widely separated scales of motion. Finally, the extent to which finite dimensional models (standard two-equation models and various generalizations) can reproduce the observed behavior is discussed
Shear flow effects on phase separation of entangled polymer blends
We introduce an entanglement model mixing rule for stress relaxation in a polymer blend to a modified Cahn-Hilliard equation of motion for concentration fluctuations in the presence of shear flow. Such an approach predicts both shear-induced mixing and demixing, depending on the relative relaxation times and plateau moduli of the two components
Phase transition in nanomagnetite
Recently, the application of nanosized magnetite particles became an area of growing interest for
their potential practical applications. Nanosized magnetite samples of 36 and 9 nm sizes were
synthesized. Special care was taken on the right stoichiometry of the magnetite particles. Mössbauer
spectroscopy measurements were made in 4.2â300 K temperature range. The temperature
dependence of the intensities of the spectral components indicated size dependent transition taking
place in a broad temperature range. For nanosized samples, the hyperfine interaction values and their
relative intensities changed above the Verwey transition temperature value of bulk megnetite. The
continuous transition indicated the formation of dendritelike granular assemblies formed during the
preparation of the samples
Instabilities of wave function monopoles in Bose-Einstein condensates
We present analytic and numerical results for a class of monopole solutions
to the two-component Gross-Pitaevski equation for a two-species Bose condensate
in an effectively two-dimensional trap. We exhibit dynamical instabilities
involving vortex production as one species pours through another, from which we
conclude that the sub-optical sharpness of potentials exerted by matter waves
makes condensates ideal tools for manipulating condensates. We also show that
there are two equally valid but drastically different hydrodynamic descriptions
of a two-component condensate, and illustrate how different phenomena may
appear simpler in each.Comment: 4 pages, 9 figures (compressed figures become legible when zoomed or
when paper is actually printed
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