345 research outputs found
Rate of convergence for a Galerkin scheme approximating a two-scale reaction-diffusion system with nonlinear transmission condition
We study a two-scale reaction-diffusion system with nonlinear reaction terms
and a nonlinear transmission condition (remotely ressembling Henry's law) posed
at air-liquid interfaces. We prove the rate of convergence of the two-scale
Galerkin method proposed in Muntean & Neuss-Radu (2009) for approximating this
system in the case when both the microstructure and macroscopic domain are
two-dimensional. The main difficulty is created by the presence of a boundary
nonlinear term entering the transmission condition. Besides using the
particular two-scale structure of the system, the ingredients of the proof
include two-scale interpolation-error estimates, an interpolation-trace
inequality, and improved regularity estimates.Comment: 14 pages, table of content
Large-time behavior of a two-scale semilinear reaction-diffusion system for concrete sulfatation
We study the large-time behavior of (weak) solutions to a two-scale
reaction-diffusion system coupled with a nonlinear ordinary differential
equations modeling the partly dissipative corrosion of concrete (/cement)-based
materials with sulfates. We prove that as the solution to the
original two-scale system converges to the corresponding two-scale stationary
system. To obtain the main result we make use essentially of the theory of
evolution equations governed by subdifferential operators of time-dependent
convex functions developed combined with a series of two-scale energy-like
time-independent estimates.Comment: 20 page
Error control for the FEM approximation of an upscaled thermo-diffusion system with Smoluchowski interactions
We analyze a coupled system of evolution equations that describes the effect
of thermal gradients on the motion and deposition of populations of
colloidal species diffusing and interacting together through Smoluchowski
production terms. This class of systems is particularly useful in studying drug
delivery, contaminant transportin complex media, as well as heat shocks
thorough permeable media. The particularity lies in the modeling of the
nonlinear and nonlocal coupling between diffusion and thermal conduction. We
investigate the semidiscrete as well as the fully discrete em a priori error
analysis of the finite elements approximation of the weak solution to a
thermo-diffusion reaction system posed in a macroscopic domain. The
mathematical techniques include energy-like estimates and compactness
arguments
Modeling micro-macro pedestrian counterflow in heterogeneous domains
We present a micro-macro strategy able to describe the dynamics of crowds in
heterogeneous media. Herein we focus on the example of pedestrian counterflow.
The main working tools include the use of mass and porosity measures together
with their transport as well as suitable application of a version of
Radon-Nikodym Theorem formulated for finite measures. Finally, we illustrate
numerically our microscopic model and emphasize the effects produced by an
implicitly defined social velocity.
Keywords: Crowd dynamics; mass measures; porosity measure; social network
Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry's law and time-dependent Dirichlet data
We study the large-time behavior of the free boundary position capturing the
one-dimensional motion of the carbonation reaction front in concrete-based
materials. We extend here our rigorous justification of the -behavior
of reaction penetration depths by including non-linear effects due to
deviations from the classical Henry's law and time-dependent Dirichlet data.Comment: 19 page
Upscaling of the dynamics of dislocation walls
We perform the discrete-to-continuum limit passage for a microscopic model
describing the time evolution of dislocations in a one dimensional setting.
This answers the related open question raised by Geers et al. in [GPPS13]. The
proof of the upscaling procedure (i.e. the discrete-to-continuum passage)
relies on the gradient flow structure of both the discrete and continuous
energies of dislocations set in a suitable evolutionary variational inequality
framework. Moreover, the convexity and -convergence of the respective
energies are properties of paramount importance for our arguments
- …