802 research outputs found
A one-dimensional Keller-Segel equation with a drift issued from the boundary
We investigate in this note the dynamics of a one-dimensional Keller-Segel
type model on the half-line. On the contrary to the classical configuration,
the chemical production term is located on the boundary. We prove, under
suitable assumptions, the following dichotomy which is reminiscent of the
two-dimensional Keller-Segel system. Solutions are global if the mass is below
the critical mass, they blow-up in finite time above the critical mass, and
they converge to some equilibrium at the critical mass. Entropy techniques are
presented which aim at providing quantitative convergence results for the
subcritical case. This note is completed with a brief introduction to a more
realistic model (still one-dimensional).Comment: short version, 8 page
Numerical simulation of the dynamics of molecular markers involved in cell polarisation
A cell is polarised when it has developed a main axis of organisation through
the reorganisation of its cytosqueleton and its intracellular organelles.
Polarisation can occur spontaneously or be triggered by external signals, like
gradients of signaling molecules ... In this work, we study mathematical models
for cell polarisation. These models are based on nonlinear convection-diffusion
equations. The nonlinearity in the transport term expresses the positive loop
between the level of protein concentration localised in a small area of the
cell membrane and the number of new proteins that will be convected to the same
area. We perform numerical simulations and we illustrate that these models are
rich enough to describe the apparition of a polarisome.Comment: 15 page
First-principles methodology for quantum transport in multiterminal junctions
We present a generalized approach for computing electron conductance and I-V
characteristics in multiterminal junctions from first-principles. Within the
framework of Keldysh theory, electron transmission is evaluated employing an
O(N) method for electronic-structure calculations. The nonequilibrium Green
function for the nonequilibrium electron density of the multiterminal junction
is computed self-consistently by solving Poisson equation after applying a
realistic bias. We illustrate the suitability of the method on two examples of
four-terminal systems, a radialene molecule connected to carbon chains and two
crossed carbon chains brought together closer and closer. We describe charge
density, potential profile, and transmission of electrons between any two
terminals. Finally, we discuss the applicability of this technique to study
complex electronic devices.Comment: Will be coming out in JCP soo
Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration
Invasion fronts in ecology are well studied but very few mathematical results
concern the case with variable motility (possibly due to mutations). Based on
an apparently simple reaction-diffusion equation, we explain the observed
phenomena of front acceleration (when the motility is unbounded) as well as
other quantitative results, such as the selection of the most motile
individuals (when the motility is bounded). The key argument for the
construction and analysis of traveling fronts is the derivation of the
dispersion relation linking the speed of the wave and the spatial decay. When
the motility is unbounded we show that the position of the front scales as
. When the mutation rate is low we show that the canonical equation
for the dynamics of the fittest trait should be stated as a PDE in our context.
It turns out to be a type of Burgers equation with source term.Comment: 7 page
Semi-empirical many-body formalism of optical absorption in nanosystems and molecules
A computationally efficient Green’s function approach is developed to evaluate the optical properties of nanostructures within a semi-empirical Hubbard model. A GW formalism is applied on top of a tight-binding and mean-field approach. The use of the GW approximation includes key parts of the many-body physics that govern the optical response of nanostructures and molecules subjected to an external electromagnetic field and that is not included in the mean-field approximation. Such description of the electron-electron correlation yields computed spectra that compare significantly better with experiment for a subset of polycyclic aromatic hydrocarbons (PAHs) considered for illustrative purpose. More generally, the method is applicable to any structure whose electronic properties can be described in first approximation within a mean-field approach and is amenable for high-throughput studies aimed at screening materials with desired optical properties
Semi-empirical many-body formalism of optical absorption in nanosystems and molecules
A computationally efficient Green's function approach is developed to
evaluate the optical properties of nanostructures using a GW formalism applied
on top of a tight-binding and mean-field Hubbard model. The use of the GW
approximation includes key parts of the many-body physics that govern the
optical response of nanostructures and molecules subjected to an external
electromagnetic field. Such description of the electron-electron correlation
yields data that are in significantly improved agreement with experiments
performed on a subset of polycyclic aromatic hydrocarbons (PAHs) considered for
illustrative purpose. More generally, the method is applicable to any structure
whose electronic properties can be described in first approximation within a
mean-field approach and is amenable for high-throughput studies aimed at
screening materials with desired optical properties
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