99 research outputs found
Modeling of smart materials with thermal effects: dynamic and quasi-static evolution
International audienceWe present a mathematical model for linear magneto-electro-thermo-elastic continua, as sensors and actuators can be thought of, and prove the well-posedness of the dynamic and quasi-static problems. The two proofs are accomplished, respectively, by means of the Hille-Yosida theory and of the Faedo-Galerkin method. A validation of the quasi-static hypothesis is provided by a nondimensionalization of the dynamic problem equations. We also hint at the study of the convergence of the solution to the dynamic problem to that to the quasi-static problem as a small parameter – the ratio of the largest propagation speed for an elastic wave in the body to the speed of light – tends to zero
An asymptotic plate model for magneto-electro-thermo-elastic sensors and actuators
International audienceWe present an asymptotic two-dimensional plate model for linear magneto-electro-thermo-elastic sensors and actuators, under the hypotheses of anisotropy and homogeneity. Four different boundary conditions pertaining to electromagnetic quantities are considered, leading to four different models: the sensor-actuator model, the actuator-sensor model, the actuator model and the sensor model. We validate the obtained two-dimensional models by proving weak convergence results. Each of the four plate problems turns out to be decoupled into a flexural problem, involving the transversal displacement of the plate, and a certain partially or totally coupled membrane problem
An exterior calculus framework for polytopal methods
We develop in this work the first polytopal complexes of differential forms.
These complexes, inspired by the Discrete De Rham and the Virtual Element
approaches, are discrete versions of the de Rham complex of differential forms
built on meshes made of general polytopal elements. Both constructions benefit
from the high-level approach of polytopal methods, which leads, on certain
meshes, to leaner constructions than the finite element method. We establish
commutation properties between the interpolators and the discrete and
continuous exterior derivatives, prove key polynomial consistency results for
the complexes, and show that their cohomologies are isomorphic to the
cohomology of the continuous de Rham complex
Gradient discretization of two-phase poro-mechanical models with discontinuous pressures at matrix fracture interfaces
We consider a two-phase Darcy flow in a fractured and deformable porous
medium for which the fractures are described as a network of planar surfaces
leading to so-called hybrid-dimensional models. The fractures are assumed open
and filled by the fluids and small deformations with a linear elastic
constitutive law are considered in the matrix. As opposed to [10], the phase
pressures are not assumed continuous at matrix fracture interfaces, which
raises new challenges in the convergence analysis related to the additional
interfacial equations and unknowns for the flow. As shown in [16, 2], unlike
single phase flow, discontinuous pressure models for two-phase flows provide a
better accuracy than continuous pressure models even for highly permeable
fractures. This is due to the fact that fractures fully filled by one phase can
act as barriers for the other phase, resulting in a pressure discontinuity at
the matrix fracture interface. The model is discretized using the gradient
discretization method [22], which covers a large class of conforming and non
conforming schemes. This framework allows for a generic convergence analysis of
the coupled model using a combination of discrete functional tools. In this
work, the gradient discretization of [10] is extended to the discontinuous
pressure model and the convergence to a weak solution is proved. Numerical
solutions provided by the continuous and discontinuous pressure models are
compared on gas injection and suction test cases using a Two-Point Flux
Approximation (TPFA) finite volume scheme for the flows and finite
elements for the mechanics.Comment: 32 pages, 11 figures. arXiv admin note: substantial text overlap with
arXiv:2004.0986
The Gradient Discretisation Method for Two-phase Discrete Fracture Matrix Models in Deformable Porous Media
International audienceWe consider a two-phase Darcy flow in a fractured porous medium consisting in a matrix flow coupled with a tangential flow in the fractures, described as a network of planar surfaces. This flow model is also coupled with the mechanical deformation of the matrix assuming that the fractures are open and filled by the fluids, as well as small deformations and a linear elastic constitutive law. The model is discretized using the gradient discretization method [3], which covers a large class of conforming and non conforming discretizations. This framework allows a generic convergence analysis of the coupled model using a combination of discrete functional tools. Here, we describe the model together with its numerical discretisation, and we state the convergence result, whose proof will be detailed in a forthcoming paper. This is, to our knowledge, the first convergence result for this type of models taking into account two-phase flows and the nonlinear poro-mechanical coupling. Previous related works consider a linear approximation obtained for a single phase flow by freezing the fracture conductivity [4]
Gradient discretization of two-phase flows coupled with mechanical deformation in fractured porous media
We consider a two-phase Darcy flow in a fractured porous medium consisting in
a matrix flow coupled with a tangential flow in the fractures, described as a
network of planar surfaces. This flow model is also coupled with the mechanical
deformation of the matrix assuming that the fractures are open and filled by
the fluids, as well as small deformations and a linear elastic constitutive
law. The model is discretized using the gradient discretization method [26],
which covers a large class of conforming and non conforming schemes. This
framework allows for a generic convergence analysis of the coupled model using
a combination of discrete functional tools. Here, we describe the model
together with its numerical discretization, and we prove a convergence result
assuming the non-degeneracy of the phase mobilities and that the discrete
solutions remain physical in the sense that, roughly speaking, the porosity
does not vanish and the fractures remain open. This is, to our knowledge, the
first convergence result for this type of models taking into account two-phase
flows in fractured porous media and the non-linear poromechanical coupling.
Previous related works consider a linear approximation obtained for a single
phase flow by freezing the fracture conductivity [36, 37]. Numerical tests
employing the Two-Point Flux Approximation (TPFA) finite volume scheme for the
flows and finite elements for the mechanical deformation are also
provided to illustrate the behavior of the solution to the model
The cosmic web of dwarf galaxies in a warm versus cold dark matter universe: mock galaxies in CDM and WDM simulations
Using cosmological simulations, we show that the cosmic web of dwarf galaxies in a warm dark matter (WDM) universe, wherein low mass halo formation is heavily suppressed, is nearly indistinguishable to that of a cold dark matter (CDM) universe whose low mass halos are not seen because galaxy formation is suppressed below some threshold mass. Low mass warm dark matter halos are suppressed nearly equally in all environments. For example, WDM voids in the galaxy distribution are neither larger nor emptier than CDM voids, once normalized to the same total galaxy number density and assuming galaxy luminosity scales with halo mass. It is thus a challenge to find hints about the dark matter particle in the cosmic web of galaxies. However, if the scatter between dwarf galaxy luminosity and halo properties is large, low mass CDM halos would sometimes host bright galaxies thereby populating voids that would be empty in WDM. Future surveys that will capture the small scale clustering in the local volume could thus help determine whether the CDM problem of the over-abundance of small halos with respect to the number density of observed dwarf galaxies has a cosmological solution or an astrophysical solution
Probing deformed commutators with macroscopic harmonic oscillators
A minimal observable length is a common feature of theories that aim to merge
quantum physics and gravity. Quantum mechanically, this concept is associated
to a nonzero minimal uncertainty in position measurements, which is encoded in
deformed commutation relations. In spite of increasing theoretical interest,
the subject suffers from the complete lack of dedicated experiments and bounds
to the deformation parameters are roughly extrapolated from indirect
measurements. As recently proposed, low-energy mechanical oscillators could
allow to reveal the effect of a modified commutator. Here we analyze the free
evolution of high quality factor micro- and nano-oscillators, spanning a wide
range of masses around the Planck mass (), and compare it with a model of deformed dynamics.
Previous limits to the parameters quantifying the commutator deformation are
substantially lowered.Comment: 11 pages, 3 figures, reference adde
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