4,883 research outputs found
Incompressible limit of mechanical model of tumor growth with viscosity
Various models of tumor growth are available in the litterature. A first
class describes the evolution of the cell number density when considered as a
continuous visco-elastic material with growth. A second class, describes the
tumor as a set and rules for the free boundary are given related to the
classical Hele-Shaw model of fluid dynamics. Following the lines of previous
papers where the material is described by a purely elastic material, or when
active cell motion is included, we make the link between the two levels of
description considering the 'stiff pressure law' limit. Even though viscosity
is a regularizing effect, new mathematical difficulties arise in the
visco-elastic case because estimates on the pressure field are weaker and do
not imply immediately compactness. For instance, traveling wave solutions and
numerical simulations show that the pressure may be discontinous in space which
is not the case for the elastic case.Comment: 17 page
A simple derivation of BV bounds for inhomogeneous relaxation systems
We consider relaxation systems of transport equations with heterogeneous
source terms and with boundary conditions, which limits are scalar conservation
laws. Classical bounds fail in this context and in particular BV estimates.
They are the most standard and simplest way to prove compactness and
convergence. We provide a novel and simple method to obtain partial BV
regularity and strong compactness in this framework. The standard notion of
entropy is not convenient either and we also indicate another, but closely
related, notion. We give two examples motivated by renal flows which consist of
2 by 2 and 3 by 3 relaxation systems with 2-velocities but the method is more
general
Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in Bilayers
We propose a one-parameter variational ansatz to describe the
tunneling-driven Abelian to non-Abelian transition in bosonic
fractional quantum Hall bilayers. This ansatz, based on exact matrix product
states, captures the low-energy physics all along the transition and allows to
probe its characteristic features. The transition is continuous, characterized
by the decoupling of antisymmetric degrees of freedom. We futhermore determine
the tunneling strength above which non-Abelian statistics should be observed
experimentally. Finally, we propose to engineer the inter-layer tunneling to
create an interface trapping a neutral chiral Majorana. We microscopically
characterize such an interface using a slightly modified model wavefunction.Comment: 5 pages, 4 Figures and Supplementary Materials. Comments are welcome
Transversal instability for the thermodiffusive reaction-diffusion system
The propagation of unstable interfaces is at the origin of remarkable
patterns that are observed in various areas of science as chemical reactions,
phase transitions, growth of bacterial colonies. Since a scalar equation
generates usually stable waves, the simplest mathematical description relies on
two by two reaction-diffusion systems. Our interest is the extension of the
Fisher/KPP equation to a two species reaction which represents reactant
concentration and temperature when used for flame propagation, bacterial
population and nutrient concentration when used in biology. We study in which
circumstances instabilities can occur and in particular the effect of
dimension. It is observed numerically that spherical waves can be unstable
depending on the coefficients. A simpler mathematical framework is to study
transversal instability, that means a one dimensional wave propagating in two
space dimensions. Then, explicit analytical formulas give explicitely the range
of paramaters for instability.Comment: 13 page
Radiation stability of EUV multilayer mirrors
This thesis describes the development and characterization of high thermal and radiation stable Si-based multilayer mirrors for their application in extreme ultraviolet lithographic steppers. Although EUV Lithography (EUVL) is an optical lithography, the reduced wavelength introduces new challenges because all materials are absorbing at 13.5 nm: The application of multilayer mirrors in EUVL requires not only the highest possible normal-incidence reflectivity but also a long-term thermal and radiation stability at operating temperatures. This requirement is most important in the case of the collector mirror of the illumination system close to the EUV source where a short-time decrease in reflectivity is most likely
Radiation stability of EUV multilayer mirrors
This thesis describes the development and characterization of high thermal and radiation stable Si-based multilayer mirrors for their application in extreme ultraviolet lithographic steppers. Although EUV Lithography (EUVL) is an optical lithography, the reduced wavelength introduces new challenges because all materials are absorbing at 13.5 nm: The application of multilayer mirrors in EUVL requires not only the highest possible normal-incidence reflectivity but also a long-term thermal and radiation stability at operating temperatures. This requirement is most important in the case of the collector mirror of the illumination system close to the EUV source where a short-time decrease in reflectivity is most likely
Radiation stability of EUV multilayer mirrors
This thesis describes the development and characterization of high thermal and radiation stable Si-based multilayer mirrors for their application in extreme ultraviolet lithographic steppers. Although EUV Lithography (EUVL) is an optical lithography, the reduced wavelength introduces new challenges because all materials are absorbing at 13.5 nm: The application of multilayer mirrors in EUVL requires not only the highest possible normal-incidence reflectivity but also a long-term thermal and radiation stability at operating temperatures. This requirement is most important in the case of the collector mirror of the illumination system close to the EUV source where a short-time decrease in reflectivity is most likely
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