908 research outputs found
Local solutions in Sobolev spaces with negative indices for the "good" Boussinesq equation
We study the local well-posedness of the initial-value problem for the
nonlinear "good" Boussinesq equation with data in Sobolev spaces \textit{}
for negative indices of .Comment: Referee comments incorporate
Origin of Lagrangian Intermittency in Drift-Wave Turbulence
The Lagrangian velocity statistics of dissipative drift-wave turbulence are
investigated. For large values of the adiabaticity (or small collisionality),
the probability density function of the Lagrangian acceleration shows
exponential tails, as opposed to the stretched exponential or algebraic tails,
generally observed for the highly intermittent acceleration of Navier-Stokes
turbulence. This exponential distribution is shown to be a robust feature
independent of the Reynolds number. For small adiabaticity, algebraic tails are
observed, suggesting the strong influence of point-vortex-like dynamics on the
acceleration. A causal connection is found between the shape of the probability
density function and the autocorrelation of the norm of the acceleration
A variational framework for flow optimization using semi-norm constraints
When considering a general system of equations describing the space-time
evolution (flow) of one or several variables, the problem of the optimization
over a finite period of time of a measure of the state variable at the final
time is a problem of great interest in many fields. Methods already exist in
order to solve this kind of optimization problem, but sometimes fail when the
constraint bounding the state vector at the initial time is not a norm, meaning
that some part of the state vector remains unbounded and might cause the
optimization procedure to diverge. In order to regularize this problem, we
propose a general method which extends the existing optimization framework in a
self-consistent manner. We first derive this framework extension, and then
apply it to a problem of interest. Our demonstration problem considers the
transient stability properties of a one-dimensional (in space) averaged
turbulent model with a space- and time-dependent model "turbulent viscosity".
We believe this work has a lot of potential applications in the fluid
dynamics domain for problems in which we want to control the influence of
separate components of the state vector in the optimization process.Comment: 30 page
Co-infection with Onchocerca volvulus and Loa loa microfilariae in central Cameroon: are these two species interacting?
Ivermectin treatment may induce severe adverse reactions in some individuals heavily infected with Loa loa. This hampers the implementation of mass ivermectin treatment against onchocerciasis in areas where Onchocerca volvulus and L. loa are co-endemic. In order to identify factors, including co-infections, which may explain the presence of high L. loa microfilaraemia in some individuals, we analysed data collected in 19 villages of central Cameroon. Two standardized skin snips and 30 mul of blood were obtained from each of 3190 participants and the microfilarial (mf) loads of both O. volvulus and L. loa were quantified. The data were analysed using multivariate hierarchical models. Individual-level variables were: age, sex, mf presence, and mf load; village-related variables included the endemicity levels for each infection. The two species show a certain degree of ecological separation in the study area. However, for a given individual host, the presence of microfilariae of one species was positively associated with the presence of microfilariae of the other (OR=1.79, 95% CI [1.43-2.24]). Among individuals harbouring Loa microfilariae, there was a slight positive relationship between the L. loa and O. volvulus mf loads which corresponded to an 11% increase in L. loa mf load per 100 O. volvulus microfilariae. Co-infection with O. volvulus is not sufficient to explain the very high L. loa mf loads harboured by some individuals
Noise and Inertia-Induced Inhomogeneity in the Distribution of Small Particles in Fluid Flows
The dynamics of small spherical neutrally buoyant particulate impurities
immersed in a two-dimensional fluid flow are known to lead to particle
accumulation in the regions of the flow in which rotation dominates over shear,
provided that the Stokes number of the particles is sufficiently small. If the
flow is viewed as a Hamiltonian dynamical system, it can be seen that the
accumulations occur in the nonchaotic parts of the phase space: the
Kolmogorov--Arnold--Moser tori. This has suggested a generalization of these
dynamics to Hamiltonian maps, dubbed a bailout embedding. In this paper we use
a bailout embedding of the standard map to mimic the dynamics of impurities
subject not only to drag but also to fluctuating forces modelled as white
noise. We find that the generation of inhomogeneities associated with the
separation of particle from fluid trajectories is enhanced by the presence of
noise, so that they appear in much broader ranges of the Stokes number than
those allowing spontaneous separation
The discrete potential Boussinesq equation and its multisoliton solutions
An alternate form of discrete potential Boussinesq equation is proposed and
its multisoliton solutions are constructed. An ultradiscrete potential
Boussinesq equation is also obtained from the discrete potential Boussinesq
equation using the ultradiscretization technique. The detail of the
multisoliton solutions is discussed by using the reduction technique. The
lattice potential Boussinesq equation derived by Nijhoff et al. is also
investigated by using the singularity confinement test. The relation between
the proposed alternate discrete potential Boussinesq equation and the lattice
potential Boussinesq equation by Nijhoff et al. is clarified.Comment: 17 pages,To appear in Applicable Analysis, Special Issue of
Continuous and Discrete Integrable System
Long-time dynamics of Rouse-Zimm polymers in dilute solutions with hydrodynamic memory
The dynamics of flexible polymers in dilute solutions is studied taking into
account the hydrodynamic memory, as a consequence of fluid inertia. As distinct
from the Rouse-Zimm (RZ) theory, the Boussinesq friction force acts on the
monomers (beads) instead of the Stokes force, and the motion of the solvent is
governed by the nonstationary Navier-Stokes equations. The obtained generalized
RZ equation is solved approximately. It is shown that the time correlation
functions describing the polymer motion essentially differ from those in the RZ
model. The mean-square displacement (MSD) of the polymer coil is at short times
\~ t^2 (instead of ~ t). At long times the MSD contains additional (to the
Einstein term) contributions, the leading of which is ~ t^(1/2). The relaxation
of the internal normal modes of the polymer differs from the traditional
exponential decay. It is displayed in the long-time tails of their correlation
functions, the longest-lived being ~ t^(-3/2) in the Rouse limit and t^(-5/2)
in the Zimm case, when the hydrodynamic interaction is strong. It is discussed
that the found peculiarities, in particular an effectively slower diffusion of
the polymer coil, should be observable in dynamic scattering experiments.Comment: 6 page
Decoupled and unidirectional asymptotic models for the propagation of internal waves
We study the relevance of various scalar equations, such as inviscid
Burgers', Korteweg-de Vries (KdV), extended KdV, and higher order equations (of
Camassa-Holm type), as asymptotic models for the propagation of internal waves
in a two-fluid system. These scalar evolution equations may be justified with
two approaches. The first method consists in approximating the flow with two
decoupled, counterpropagating waves, each one satisfying such an equation. One
also recovers homologous equations when focusing on a given direction of
propagation, and seeking unidirectional approximate solutions. This second
justification is more restrictive as for the admissible initial data, but
yields greater accuracy. Additionally, we present several new coupled
asymptotic models: a Green-Naghdi type model, its simplified version in the
so-called Camassa-Holm regime, and a weakly decoupled model. All of the models
are rigorously justified in the sense of consistency
Commuting Flows and Conservation Laws for Noncommutative Lax Hierarchies
We discuss commuting flows and conservation laws for Lax hierarchies on
noncommutative spaces in the framework of the Sato theory. On commutative
spaces, the Sato theory has revealed essential aspects of the integrability for
wide class of soliton equations which are derived from the Lax hierarchies in
terms of pseudo-differential operators. Noncommutative extension of the Sato
theory has been already studied by the author and Kouichi Toda, and the
existence of various noncommutative Lax hierarchies are guaranteed. In the
present paper, we present conservation laws for the noncommutative Lax
hierarchies with both space-space and space-time noncommutativities and prove
the existence of infinite number of conserved densities. We also give the
explicit representations of them in terms of Lax operators. Our results include
noncommutative versions of KP, KdV, Boussinesq, coupled KdV, Sawada-Kotera,
modified KdV equations and so on.Comment: 22 pages, LaTeX, v2: typos corrected, references added, version to
appear in JM
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