58 research outputs found
On the role of the Knudsen layer in rapid granular flows
A combination of molecular-dynamics simulations, theoretical predictions, and
previous experiments are used in a two-part study to determine the role of the
Knudsen layer in rapid granular flows. First, a robust criterion for the
identification of the thickness of the Knudsen layer is established: a rapid
deterioration in Navier-Stokes-order prediction of the heat flux is found to
occur in the Knudsen layer. For (experimental) systems in which heat flux
measurements are not easily obtained, a rule-of-thumb for estimating the
Knudsen layer thickness follows, namely that such effects are evident within
2.5 (local) mean free paths of a given boundary. Second, comparisons of
simulation and experimental data with Navier-Stokes order theory are used to
provide a measure as to when Knudsen layer effects become non-negligible.
Specifically, predictions that do not account for the presence of a Knudsen
layer appear reliable for Knudsen layers collectively composing up to 20% of
the domain, whereas deterioration of such predictions becomes apparent when the
domain is fully comprised of the Knudsen layer.Comment: 9 figures, accepted to Journal of Fluid Mechanic
Normalizations with exponentially small remainders for nonautonomous analytic periodic vector fields
In this paper we deal with analytic nonautonomous vector fields with a
periodic time-dependancy, that we study near an equilibrium point. In a first
part, we assume that the linearized system is split in two invariant subspaces
E0 and E1. Under light diophantine conditions on the eigenvalues of the linear
part, we prove that there is a polynomial change of coordinates in E1 allowing
to eliminate up to a finite polynomial order all terms depending only on the
coordinate u0 of E0 in the E1 component of the vector field. We moreover show
that, optimizing the choice of the degree of the polynomial change of
coordinates, we get an exponentially small remainder. In the second part, we
prove a normal form theorem with exponentially small remainder. Similar
theorems have been proved before in the autonomous case : this paper
generalizes those results to the nonautonomous periodic case
Memory functions and Correlations in Additive Binary Markov Chains
A theory of additive Markov chains with long-range memory, proposed earlier
in Phys. Rev. E 68, 06117 (2003), is developed and used to describe statistical
properties of long-range correlated systems. The convenient characteristics of
such systems, a memory function, and its relation to the correlation properties
of the systems are examined. Various methods for finding the memory function
via the correlation function are proposed. The inverse problem (calculation of
the correlation function by means of the prescribed memory function) is also
solved. This is demonstrated for the analytically solvable model of the system
with a step-wise memory function.Comment: 11 pages, 5 figure
On the Lagrangian Dynamics of Atmospheric Zonal Jets and the Permeability of the Stratospheric Polar Vortex
The Lagrangian dynamics of zonal jets in the atmosphere are considered, with
particular attention paid to explaining why, under commonly encountered
conditions, zonal jets serve as barriers to meridional transport. The velocity
field is assumed to be two-dimensional and incompressible, and composed of a
steady zonal flow with an isolated maximum (a zonal jet) on which two or more
travelling Rossby waves are superimposed. The associated Lagrangian motion is
studied with the aid of KAM (Kolmogorov--Arnold--Moser) theory, including
nontrivial extensions of well-known results. These extensions include
applicability of the theory when the usual statements of nondegeneracy are
violated, and applicability of the theory to multiply periodic systems,
including the absence of Arnold diffusion in such systems. These results,
together with numerical simulations based on a model system, provide an
explanation of the mechanism by which zonal jets serve as barriers to
meridional transport of passive tracers under commonly encountered conditions.
Causes for the breakdown of such a barrier are discussed. It is argued that a
barrier of this type accounts for the sharp boundary of the Antarctic ozone
hole at the perimeter of the stratospheric polar vortex in the austral spring.Comment: Submitted to Journal of the Atmospheric Science
Congestion in a macroscopic model of self-driven particles modeling gregariousness
International audienceWe analyze a macroscopic model with a maximal density constraint which describes short range repulsion in biological systems. This system aims at modeling finite-size particles which cannot overlap and repel each other when they are too close. The parts of the fluid where the maximal density is reached behave like incompressible fluids while lower density regions are compressible. This paper investigates the transition between the compressible and incompressible regions. To capture this transition, we study a one-dimensional Riemann problem and introduce a perturbation problem which regularizes the compressible-incompressible transition. Specific difficulties related to the non-conservativity of the problem are discussed
Replacing the Ethylmalonyl-CoA Pathway with the Glyoxylate Shunt Provides Metabolic Flexibility in the Central Carbon Metabolism of Methylobacterium extorquens AM1
The ethylmalonyl-CoA pathway (EMCP) is an anaplerotic reaction sequence in the central carbon metabolism of numerous Proteo- and Actinobacteria. The pathway features several CoA-bound mono- and dicarboxylic acids that are of interest as platform chemicals for the chemical industry. The EMCP, however, is essential for growth on C1 and C2 carbon substrates and therefore cannot be simply interrupted to drain these intermediates. In this study, we aimed at reengineering central carbon metabolism of the Alphaproteobacterium Methylobacterium extorquens AM1 for the specific production of EMCP derivatives in the supernatant. Establishing a heterologous glyoxylate shunt in M. extorquens AM1 restored wild type-like growth in several EMCP knockout strains on defined minimal medium with acetate as carbon source. We further engineered one of these strains that carried a deletion of the gene encoding crotonyl-CoA carboxylase/reductase to demonstrate in a proof-of-concept the specific production of crotonic acid in the supernatant on a defined minimal medium. Our experiments demonstrate that it is in principle possible to further exploit the EMCP by establishing an alternative central carbon metabolic pathway in M. extorquens AM1, opening many possibilities for the biotechnological production of EMCP-derived compounds in future
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