1,980 research outputs found
Statistical mechanics of two-dimensional Euler flows and minimum enstrophy states
A simplified thermodynamic approach of the incompressible 2D Euler equation
is considered based on the conservation of energy, circulation and microscopic
enstrophy. Statistical equilibrium states are obtained by maximizing the
Miller-Robert-Sommeria (MRS) entropy under these sole constraints. The
vorticity fluctuations are Gaussian while the mean flow is characterized by a
linear relationship. Furthermore, the maximization of
entropy at fixed energy, circulation and microscopic enstrophy is equivalent to
the minimization of macroscopic enstrophy at fixed energy and circulation. This
provides a justification of the minimum enstrophy principle from statistical
mechanics when only the microscopic enstrophy is conserved among the infinite
class of Casimir constraints. A new class of relaxation equations towards the
statistical equilibrium state is derived. These equations can provide an
effective description of the dynamics towards equilibrium or serve as numerical
algorithms to determine maximum entropy or minimum enstrophy states. We use
these relaxation equations to study geometry induced phase transitions in
rectangular domains. In particular, we illustrate with the relaxation equations
the transition between monopoles and dipoles predicted by Chavanis and Sommeria
[J. Fluid. Mech. 314, 267 (1996)]. We take into account stable as well as
metastable states and show that metastable states are robust and have negative
specific heats. This is the first evidence of negative specific heats in that
context. We also argue that saddle points of entropy can be long-lived and play
a role in the dynamics because the system may not spontaneously generate the
perturbations that destabilize them.Comment: 26 pages, 10 figure
Intrusion and extrusion of water in hydrophobic mesopores
We present experimental and theoretical results on intrusion-extrusion cycles
of water in hydrophobic mesoporous materials, characterized by independent
cylindrical pores. The intrusion, which takes place above the bulk saturation
pressure, can be well described using a macroscopic capillary model. Once the
material is saturated with water, extrusion takes place upon reduction of the
externally applied pressure; Our results for the extrusion pressure can only be
understood by assuming that the limiting extrusion mechanism is the nucleation
of a vapour bubble inside the pores. A comparison of calculated and
experimental nucleation pressures shows that a proper inclusion of line tension
effects is necessary to account for the observed values of nucleation barriers.
Negative line tensions of order are found for our
system, in reasonable agreement with other experimental estimates of this
quantity
Analysis of an operator-differential model for magnetostrictive energy harvesting
We present a model of, and analysis of an optimization problem for, a magnetostrictive harvesting device which converts mechanical energy of the repetitive process such as vibrations of the smart material to electrical energy that is then supplied to an electric load. The model combines a lumped differential equation for a simple electronic circuit with an operator model for the complex constitutive law of the magnetostrictive material. The operator based on the formalism of the phenomenological Preisach model describes nonlinear saturation effects and hysteresis losses typical of magnetostrictive materials in a thermodynamically consistent fashion. We prove well-posedness of the full operator-differential system and establish global asymptotic stability of the periodic regime under periodic mechanical forcing that represents mechanical vibrations due to varying environmental conditions. Then we show the existence of an optimal solution for the problem of maximization of the output power with respect to a set of controllable parameters (for the periodically forced system). Analytical results are illustrated with numerical examples of an optimal solution
Piecewise linear car-following modeling
We present a traffic model that extends the linear car-following model as
well as the min-plus traffic model (a model based on the min-plus algebra). A
discrete-time car-dynamics describing the traffic on a 1-lane road without
passing is interpreted as a dynamic programming equation of a stochastic
optimal control problem of a Markov chain. This variational formulation permits
to characterize the stability of the car-dynamics and to calculte the
stationary regimes when they exist. The model is based on a piecewise linear
approximation of the fundamental traffic diagram.Comment: 19 pages, 3 figure
Analysis of an operator-differential model for magnetostrictive energy harvesting
We present a model of, and analysis of an optimization problem for, a
magnetostrictive harvesting device which converts mechanical energy of the
repetitive process such as vibrations of the smart material to electrical
energy that is then supplied to an electric load. The model combines a lumped
differential equation for a simple electronic circuit with an operator model
for the complex constitutive law of the magnetostrictive material. The
operator based on the formalism of the phenomenological Preisach model
describes nonlinear saturation effects and hysteresis losses typical of
magnetostrictive materials in a thermodynamically consistent fashion. We
prove well-posedness of the full operatordifferential system and establish
global asymptotic stability of the periodic regime under periodic mechanical
forcing that represents mechanical vibrations due to varying environmental
conditions. Then we show the existence of an optimal solution for the problem
of maximization of the output power with respect to a set of controllable
parameters (for the periodically forced system). Analytical results are
illustrated with numerical examples of an optimal solution
Mathematical models of martensitic microstructure
Martensitic microstructures are studied using variational models based on nonlinear elasticity. Some relevant mathematical tools from nonlinear analysis are described, and applications given to austenite-martensite interfaces and related topics
A rate-independent model for the isothermal quasi-static evolution of shape-memory materials
This note addresses a three-dimensional model for isothermal stress-induced
transformation in shape-memory polycrystalline materials. We treat the problem
within the framework of the energetic formulation of rate-independent processes
and investigate existence and continuous dependence issues at both the
constitutive relation and quasi-static evolution level. Moreover, we focus on
time and space approximation as well as on regularization and parameter
asymptotics.Comment: 33 pages, 3 figure
Reactive Flow and Transport Through Complex Systems
The meeting focused on mathematical aspects of reactive flow, diffusion and transport through complex systems. The research interest of the participants varied from physical modeling using PDEs, mathematical modeling using upscaling and homogenization, numerical analysis of PDEs describing reactive transport, PDEs from fluid mechanics, computational methods for random media and computational multiscale methods
Reactive Flows in Deformable, Complex Media
Many processes of highest actuality in the real life are described through systems of equations posed in complex domains. Of particular interest is the situation when the domain is variable, undergoing deformations that depend on the unknown quantities of the model. Such kind of problems are encountered as mathematical models in the subsurface, or biological systems. Such models include various processes at different scales, and the key issue is to integrate the domain deformation in the multi-scale context. Having this as the background theme, this workshop focused on novel techniques and ideas in the analysis, the numerical discretization and the upscaling of such problems, as well as on applications of major societal relevance today
- âŠ