520 research outputs found
Reactive Turbulent Flow in Low-Dimensional, Disordered Media
We analyze the reactions and
occurring in a model of turbulent flow in two dimensions. We find the reactant
concentrations at long times, using a field-theoretic renormalization group
analysis. We find a variety of interesting behavior, including, in the presence
of potential disorder, decay rates faster than that for well-mixed reactions.Comment: 6 pages, 4 figures. To appear in Phys. Rev.
Exact solution of the one-dimensional ballistic aggregation
An exact expression for the mass distribution of the ballistic
aggregation model in one dimension is derived in the long time regime. It is
shown that it obeys scaling with a scaling
function for and for
. Relevance of these results to Burgers turbulence is discussed.Comment: 11 pages, 2 Postscript figure
On the strong anomalous diffusion
The superdiffusion behavior, i.e. , with , in general is not completely characherized by a unique exponent. We study
some systems exhibiting strong anomalous diffusion, i.e. where and is not a linear function of .
This feature is different from the weak superdiffusion regime, i.e.
, as in random shear flows. The strong anomalous diffusion
can be generated by nontrivial chaotic dynamics, e.g. Lagrangian motion in
time-dependent incompressible velocity fields, symplectic maps and
intermittent maps. Typically the function is piecewise linear. This
corresponds to two mechanisms: a weak anomalous diffusion for the typical
events and a ballistic transport for the rare excursions. In order to have
strong anomalous diffusion one needs a violation of the hypothesis of the
central limit theorem, this happens only in a very narrow region of the control
parameters space.Comment: 27 pages, 14 figure
Analytic results and weighted Monte Carlo simulations for CDO pricing
We explore the possibilities of importance sampling in the Monte Carlo
pricing of a structured credit derivative referred to as Collateralized Debt
Obligation (CDO). Modeling a CDO contract is challenging, since it depends on a
pool of (typically about 100) assets, Monte Carlo simulations are often the
only feasible approach to pricing. Variance reduction techniques are therefore
of great importance. This paper presents an exact analytic solution using
Laplace-transform and MC importance sampling results for an easily tractable
intensity-based model of the CDO, namely the compound Poissonian. Furthermore
analytic formulae are derived for the reweighting efficiency. The computational
gain is appealing, nevertheless, even in this basic scheme, a phase transition
can be found, rendering some parameter regimes out of reach. A
model-independent transform approach is also presented for CDO pricing.Comment: 12 pages, 9 figure
Dispersion Coefficients by a Field-Theoretic Renormalization of Fluid Mechanics
We consider subtle correlations in the scattering of fluid by randomly placed
obstacles, which have been suggested to lead to a diverging dispersion
coefficient at long times for high Peclet numbers, in contrast to finite
mean-field predictions. We develop a new master equation description of the
fluid mechanics that incorporates the physically relevant fluctuations, and we
treat those fluctuations by a renormalization group procedure. We find a finite
dispersion coefficient at low volume fraction of disorder and high Peclet
numbers.Comment: 4 pages, 1 figure; to appear in Phys. Rev. Let
Enhacement in the dymanic response of a viscoelastic fluid flowing through a longitudinally vibrating tube
We analyzed effects of elasticity on the dynamics of fluids in porous media
by studying a flow of a Maxwell fluid in a tube, which oscillates
longitudinally and is subject to oscillatory pressure gradient. The present
study investigates novelties brought about into the classic Biot's theory of
propagation of elastic waves in a fluid-saturated porous solid by inclusion of
non-Newtonian effects that are important, for example, for hydrocarbons. Using
the time Fourier transform and transforming the problem into the frequency
domain, we calculated: (A) the dynamic permeability and (B) the function
that measures the deviation from Poiseuille flow friction as a
function of frequency parameter . This provides a more complete theory
of flow of Maxwell fluid through the longitudinally oscillating cylindrical
tube with the oscillating pressure gradient, which has important practical
applications. This study has clearly shown transition from dissipative to
elastic regime in which sharp enhancements (resonances) of the flow are found
Flame Enhancement and Quenching in Fluid Flows
We perform direct numerical simulations (DNS) of an advected scalar field
which diffuses and reacts according to a nonlinear reaction law. The objective
is to study how the bulk burning rate of the reaction is affected by an imposed
flow. In particular, we are interested in comparing the numerical results with
recently predicted analytical upper and lower bounds. We focus on reaction
enhancement and quenching phenomena for two classes of imposed model flows with
different geometries: periodic shear flow and cellular flow. We are primarily
interested in the fast advection regime. We find that the bulk burning rate v
in a shear flow satisfies v ~ a*U+b where U is the typical flow velocity and a
is a constant depending on the relationship between the oscillation length
scale of the flow and laminar front thickness. For cellular flow, we obtain v ~
U^{1/4}. We also study flame extinction (quenching) for an ignition-type
reaction law and compactly supported initial data for the scalar field. We find
that in a shear flow the flame of the size W can be typically quenched by a
flow with amplitude U ~ alpha*W. The constant alpha depends on the geometry of
the flow and tends to infinity if the flow profile has a plateau larger than a
critical size. In a cellular flow, we find that the advection strength required
for quenching is U ~ W^4 if the cell size is smaller than a critical value.Comment: 14 pages, 20 figures, revtex4, submitted to Combustion Theory and
Modellin
Diffusive transport and self-consistent dynamics in coupled maps
The study of diffusion in Hamiltonian systems has been a problem of interest
for a number of years.
In this paper we explore the influence of self-consistency on the diffusion
properties of systems described by coupled symplectic maps. Self-consistency,
i.e. the back-influence of the transported quantity on the velocity field of
the driving flow, despite of its critical importance, is usually overlooked in
the description of realistic systems, for example in plasma physics. We propose
a class of self-consistent models consisting of an ensemble of maps globally
coupled through a mean field. Depending on the kind of coupling, two different
general types of self-consistent maps are considered: maps coupled to the field
only through the phase, and fully coupled maps, i.e. through the phase and the
amplitude of the external field. The analogies and differences of the diffusion
properties of these two kinds of maps are discussed in detail.Comment: 13 pages, 14 figure
The Navier wall law at a boundary with random roughness
We consider the Navier-Stokes equation in a domain with irregular boundaries.
The irregularity is modeled by a spatially homogeneous random process, with
typical size \eps \ll 1. In a parent paper, we derived a homogenized boundary
condition of Navier type as \eps \to 0. We show here that for a large class
of boundaries, this Navier condition provides a O(\eps^{3/2} |\ln
\eps|^{1/2}) approximation in , instead of O(\eps^{3/2}) for periodic
irregularities. Our result relies on the study of an auxiliary boundary layer
system. Decay properties of this boundary layer are deduced from a central
limit theorem for dependent variables
Malvinas-slope water intrusions on the northern Patagonia continental shelf
The Patagonia continental shelf located off southeastern South America is bounded offshore by the Malvinas Current, which extends northward from northern Drake Passage (~55&deg; S) to nearly 38&deg; S. The transition between relatively warm-fresh shelf waters and Subantarctic Waters from the western boundary current is characterized by a thermohaline front extending nearly 2500 km. We use satellite derived sea surface temperature, and chlorophyll-<I>a</I> data combined with hydrographic and surface drifter data to document the intrusions of slope waters onto the continental shelf near 41&deg; S. These intrusions create vertically coherent localized negative temperature and positive salinity anomalies extending onshore about 150 km from the shelf break. The region is associated with a center of action of the first mode of non-seasonal sea surface temperature variability and also relatively high chlorophyll-<I>a</I> variability, suggesting that the intrusions are important in promoting the local development of phytoplankton. The generation of slope water penetrations at this location may be triggered by the inshore excursion of the 100 m isobath, which appears to steer the Malvinas Current waters over the outer shelf
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