795 research outputs found
Multi-Scale Statistical Approach of the Elastic and Thermal Behavior of a Thermoplastic Polyamid-Glass Fiber Composite
The strong heterogeneity and the anisotropy of composite materials require a rigorous and precise analysis as a result of their impact on local properties. First, mechanical tests are performed to determine the macroscopical behavior of a polyamid glass fiber composite. Then we focus on the influence of the heterogeneities of the microstructure on thermal and mechanical properties from finite element calculations on the real microstructure, after plane strain assumptions. 100 images in 10 different sizes (50, 100, 150, 200, 250, 300, 350, 400, 450, 600 pixels) are analysed. The influence of the area fraction and the spatial arrangement of fibers is then established. For the thermal conductivity and the bulk modulus the fiber area fraction is the most important factor. These properties are improved by increasing the area fraction. On the other hand, for the shear modulus, the fibers spatial arrangement plays the paramount role if the size of the microstructure is smaller than the RVE. Therefore, to make a good prediction from a multi-scale approach the knowledge of the RVE is fundamental. By a statistical approach and a numerical homogenization method, we determine the RVE of the composite for the elastic behavior (shear and bulk moduli), the thermal behavior (thermal conductivity), and for the area fraction. There is a relatively good agreement between the effective properties of this RVE and the experimental macroscopical behavior. These effective properties are estimated by the Hashin-Shtrikman lower bound
Lognormal scale invariant random measures
In this article, we consider the continuous analog of the celebrated
Mandelbrot star equation with lognormal weights. Mandelbrot introduced this
equation to characterize the law of multiplicative cascades. We show existence
and uniqueness of measures satisfying the aforementioned continuous equation;
these measures fall under the scope of the Gaussian multiplicative chaos theory
developed by J.P. Kahane in 1985 (or possibly extensions of this theory). As a
by product, we also obtain an explicit characterization of the covariance
structure of these measures. We also prove that qualitative properties such as
long-range independence or isotropy can be read off the equation.Comment: 31 pages; Probability Theory and Related Fields (2012) electronic
versio
Pauli spin susceptibility of a strongly correlated two-dimensional electron liquid
Thermodynamic measurements reveal that the Pauli spin susceptibility of
strongly correlated two-dimensional electrons in silicon grows critically at
low electron densities - behavior that is characteristic of the existence of a
phase transition.Comment: As publishe
Organisation of joints and faults from 1-cm to 100-km scales revealed by optimized anisotropic wavelet coefficient method and multifractal analysis
International audienceThe classical method of statistical physics deduces the macroscopic behaviour of a system from the organization and interactions of its microscopical constituents. This kind of problem can often be solved using procedures deduced from the Renormalization Group Theory, but in some cases, the basic microscopic rail are unknown and one has to deal only with the intrinsic geometry. The wavelet analysis concept appears to be particularly adapted to this kind of situation as it highlights details of a set at a given analyzed scale. As fractures and faults generally define highly anisotropic fields, we defined a new renormalization procedure based on the use of anisotropic wavelets. This approach consists of finding an optimum filter will maximizes wavelet coefficients at each point of the fie] Its intrinsic definition allows us to compute a rose diagram of the main structural directions present in t field at every scale. Scaling properties are determine using a multifractal box-counting analysis improved take account of samples with irregular geometry and finite size. In addition, we present histograms of fault length distribution. Our main observation is that different geometries and scaling laws hold for different rang of scales, separated by boundaries that correlate well with thicknesses of lithological units that constitute the continental crust. At scales involving the deformation of the crystalline crust, we find that faulting displays some singularities similar to those commonly observed in Diffusion- Limited Aggregation processes
Three-dimensional writing inside silicon using a 2-µm picosecond fiber laser
International audienc
Smooth stable and unstable manifolds for stochastic partial differential equations
Invariant manifolds are fundamental tools for describing and understanding
nonlinear dynamics. In this paper, we present a theory of stable and unstable
manifolds for infinite dimensional random dynamical systems generated by a
class of stochastic partial differential equations. We first show the existence
of Lipschitz continuous stable and unstable manifolds by the Lyapunov-Perron's
method. Then, we prove the smoothness of these invariant manifolds
Universality in fully developed turbulence
We extend the numerical simulations of She et al. [Phys.\ Rev.\ Lett.\ 70,
3251 (1993)] of highly turbulent flow with Taylor-Reynolds number
up to , employing a reduced wave
vector set method (introduced earlier) to approximately solve the Navier-Stokes
equation. First, also for these extremely high Reynolds numbers ,
the energy spectra as well as the higher moments -- when scaled by the spectral
intensity at the wave number of peak dissipation -- can be described by
{\it one universal} function of for all . Second, the ISR
scaling exponents of this universal function are in agreement with
the 1941 Kolmogorov theory (the better, the large is), as is the
dependence of . Only around viscous damping leads to
slight energy pileup in the spectra, as in the experimental data (bottleneck
phenomenon).Comment: 14 pages, Latex, 5 figures (on request), 3 tables, submitted to Phys.
Rev.
Wind Energy and the Turbulent Nature of the Atmospheric Boundary Layer
Wind turbines operate in the atmospheric boundary layer, where they are
exposed to the turbulent atmospheric flows. As the response time of wind
turbine is typically in the range of seconds, they are affected by the small
scale intermittent properties of the turbulent wind. Consequently, basic
features which are known for small-scale homogeneous isotropic turbulence, and
in particular the well-known intermittency problem, have an important impact on
the wind energy conversion process. We report on basic research results
concerning the small-scale intermittent properties of atmospheric flows and
their impact on the wind energy conversion process. The analysis of wind data
shows strongly intermittent statistics of wind fluctuations. To achieve
numerical modeling a data-driven superposition model is proposed. For the
experimental reproduction and adjustment of intermittent flows a so-called
active grid setup is presented. Its ability is shown to generate reproducible
properties of atmospheric flows on the smaller scales of the laboratory
conditions of a wind tunnel. As an application example the response dynamics of
different anemometer types are tested. To achieve a proper understanding of the
impact of intermittent turbulent inflow properties on wind turbines we present
methods of numerical and stochastic modeling, and compare the results to
measurement data. As a summarizing result we find that atmospheric turbulence
imposes its intermittent features on the complete wind energy conversion
process. Intermittent turbulence features are not only present in atmospheric
wind, but are also dominant in the loads on the turbine, i.e. rotor torque and
thrust, and in the electrical power output signal. We conclude that profound
knowledge of turbulent statistics and the application of suitable numerical as
well as experimental methods are necessary to grasp these unique features (...)Comment: Accepted by the Journal of Turbulence on May 17, 201
Self-Organized States in Cellular Automata: Exact Solution
The spatial structure, fluctuations as well as all state probabilities of
self-organized (steady) states of cellular automata can be found (almost)
exactly and {\em explicitly} from their Markovian dynamics. The method is shown
on an example of a natural sand pile model with a gradient threshold.Comment: 4 pages (REVTeX), incl. 2 figures (PostScript
Rayleigh-Taylor instability of crystallization waves at the superfluid-solid 4He interface
At the superfluid-solid 4He interface there exist crystallization waves
having much in common with gravitational-capillary waves at the interface
between two normal fluids. The Rayleigh-Taylor instability is an instability of
the interface which can be realized when the lighter fluid is propelling the
heavier one. We investigate here the analogues of the Rayleigh-Taylor
instability for the superfluid-solid 4He interface. In the case of a uniformly
accelerated interface the instability occurs only for a growing solid phase
when the magnitude of the acceleration exceeds some critical value independent
of the surface stiffness. For the Richtmyer-Meshkov limiting case of an
impulsively accelerated interface, the onset of instability does not depend on
the sign of the interface acceleration. In both cases the effect of
crystallization wave damping is to reduce the perturbation growth-rate of the
Taylor unstable interface.Comment: 8 pages, 2 figures, RevTe
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