713 research outputs found
Limiting problems for a nonstandard viscous Cahn--Hilliard system with dynamic boundary conditions
This note is concerned with a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by boundary and initial conditions. The system arises from a model of two-species phase segregation on an atomic lattice and was introduced by Podio-Guidugli in Ric. Mat. 55 (2006), pp.105--118. The two unknowns are the phase parameter and the chemical potential. In contrast to previous investigations about this PDE system, we consider here a dynamic boundary condition for the phase variable that involves the Laplace-Beltrami operator and models an additional nonconserving phase transition occurring on the surface of the domain. We are interested to some asymptotic analysis and first discuss the asymptotic limit of the system as the viscosity coefficient of the order parameter equation tends to 0: the convergence of solutions to the corresponding solutions for the limit problem is proven. Then, we study the long-time behavior of the system for both problems, with positive or zero viscosity coefficient, and characterize the omega-limit set in both cases
On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities
We study a non-local variant of a diffuse interface model proposed by
Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical
species acting as nutrient. The system consists of a Cahn--Hilliard equation
coupled to a reaction-diffusion equation. For non-degenerate mobilities and
smooth potentials, we derive well-posedness results, which are the non-local
analogue of those obtained in Frigeri et al. (European J. Appl. Math. 2015).
Furthermore, we establish existence of weak solutions for the case of
degenerate mobilities and singular potentials, which serves to confine the
order parameter to its physically relevant interval. Due to the non-local
nature of the equations, under additional assumptions continuous dependence on
initial data can also be shown.Comment: 28 page
Longtime behavior of nonlocal Cahn-Hilliard equations
Here we consider the nonlocal Cahn-Hilliard equation with constant mobility
in a bounded domain. We prove that the associated dynamical system has an
exponential attractor, provided that the potential is regular. In order to do
that a crucial step is showing the eventual boundedness of the order parameter
uniformly with respect to the initial datum. This is obtained through an
Alikakos-Moser type argument. We establish a similar result for the viscous
nonlocal Cahn-Hilliard equation with singular (e.g., logarithmic) potential. In
this case the validity of the so-called separation property is crucial. We also
discuss the convergence of a solution to a single stationary state. The
separation property in the nonviscous case is known to hold when the mobility
degenerates at the pure phases in a proper way and the potential is of
logarithmic type. Thus, the existence of an exponential attractor can be proven
in this case as well
On a Cahn--Hilliard--Darcy system for tumour growth with solution dependent source terms
We study the existence of weak solutions to a mixture model for tumour growth
that consists of a Cahn--Hilliard--Darcy system coupled with an elliptic
reaction-diffusion equation. The Darcy law gives rise to an elliptic equation
for the pressure that is coupled to the convective Cahn--Hilliard equation
through convective and source terms. Both Dirichlet and Robin boundary
conditions are considered for the pressure variable, which allows for the
source terms to be dependent on the solution variables.Comment: 18 pages, changed proof from fixed point argument to Galerkin
approximatio
Optimal control for a phase field system with a possibly singular potential
In this paper we study a distributed control problem for a phase field system of Caginalp type with logarithmic potential. The main aim of this work would be to force the location of the diffuse interface to be as close as possible to a prescribed set. However, due to the discontinuous character of the cost functional, we have to approximate it by a regular one and, in this case, we solve the associated control problem and derive the related first order necessary optimality conditions
Chaotic Scattering in Heavy--Ion Reactions
We discuss the relevance of chaotic scattering in heavy--ion reactions at
energies around the Coulomb barrier. A model in two and three dimensions which
takes into account rotational degrees of freedom is discussed both classically
and quantum-mechanically. The typical chaotic features found in this
description of heavy-ion collisions are connected with the anomalous behaviour
of several experimental data.Comment: 35 pages in RevTex (version 3.0) plus 27 PostScript figures
obtainable by anonymous ftp from VAXFCT.CT.INFN.IT in directory kaos. Fig. 1
upon request to the authors. To be published in the October Focus issue on
chaotic scattering of CHAO
Relação entre Triatoma infestans, aves domésticas e o homem num povoado de Santiago del Estero, Argentina
Use of transgenic Aedes aegypti in Brazil: risk perception and assessment.
The OX513A strain of Aedes aegypti, which was developed by the British company Oxitec, expresses a self-limiting transgene that prevents larvae from developing to adulthood. In April 2014, the Brazilian National Technical Commission on Biosafety completed a risk assessment of OX513A and concluded that the strain did not present new biological risks to humans or the environment and could be released in Brazil. At that point, Brazil became the first country to approve the unconstrained release of a genetically modified mosquito. During the assessment, the commission produced a comprehensive list of ? and systematically analysed ? the perceived hazards. Such hazards included the potential survival to adulthood of immature stages carrying the transgene ? should the transgene fail to be expressed or be turned off by exposure to sufficient environmental tetracycline. Other perceived hazards included the potential allergenicity and/or toxicity of the proteins expressed by the gene, the potential for gene flow or increased transmission of human pathogens and the occupation of vacant breeding sites by other vector species. The Zika epidemic both elevated the perceived importance of Ae. aegypti as a vector ? among policy-makers and regulators as well as the general public ? and increased concerns over the release of males of the OX513A strain. We have therefore reassessed the potential hazards. We found that release of the transgenic mosquitoes would still be both safe and of great potential value in the control of diseases spread by Ae. aegypti, such as the chikungunya, dengue and Zika virus disease
Incorporating Inductances in Tissue-Scale Models of Cardiac Electrophysiology
In standard models of cardiac electrophysiology, including the bidomain and
monodomain models, local perturbations can propagate at infinite speed. We
address this unrealistic property by developing a hyperbolic bidomain model
that is based on a generalization of Ohm's law with a Cattaneo-type model for
the fluxes. Further, we obtain a hyperbolic monodomain model in the case that
the intracellular and extracellular conductivity tensors have the same
anisotropy ratio. In one spatial dimension, the hyperbolic monodomain model is
equivalent to a cable model that includes axial inductances, and the relaxation
times of the Cattaneo fluxes are strictly related to these inductances. A
purely linear analysis shows that the inductances are negligible, but models of
cardiac electrophysiology are highly nonlinear, and linear predictions may not
capture the fully nonlinear dynamics. In fact, contrary to the linear analysis,
we show that for simple nonlinear ionic models, an increase in conduction
velocity is obtained for small and moderate values of the relaxation time. A
similar behavior is also demonstrated with biophysically detailed ionic models.
Using the Fenton-Karma model along with a low-order finite element spatial
discretization, we numerically analyze differences between the standard
monodomain model and the hyperbolic monodomain model. In a simple benchmark
test, we show that the propagation of the action potential is strongly
influenced by the alignment of the fibers with respect to the mesh in both the
parabolic and hyperbolic models when using relatively coarse spatial
discretizations. Accurate predictions of the conduction velocity require
computational mesh spacings on the order of a single cardiac cell. We also
compare the two formulations in the case of spiral break up and atrial
fibrillation in an anatomically detailed model of the left atrium, and [...].Comment: 20 pages, 12 figure
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