17 research outputs found
Global solutions for a hyperbolic-parabolic system of chemotaxis
We study a hyperbolic-parabolic model of chemotaxis in dimensions one and
two. In particular, we prove the global existence of classical solutions in
certain dissipation regimes
Mathematical description of bacterial traveling pulses
The Keller-Segel system has been widely proposed as a model for bacterial
waves driven by chemotactic processes. Current experiments on {\em E. coli}
have shown precise structure of traveling pulses. We present here an
alternative mathematical description of traveling pulses at a macroscopic
scale. This modeling task is complemented with numerical simulations in
accordance with the experimental observations. Our model is derived from an
accurate kinetic description of the mesoscopic run-and-tumble process performed
by bacteria. This model can account for recent experimental observations with
{\em E. coli}. Qualitative agreements include the asymmetry of the pulse and
transition in the collective behaviour (clustered motion versus dispersion). In
addition we can capture quantitatively the main characteristics of the pulse
such as the speed and the relative size of tails. This work opens several
experimental and theoretical perspectives. Coefficients at the macroscopic
level are derived from considerations at the cellular scale. For instance the
stiffness of the signal integration process turns out to have a strong effect
on collective motion. Furthermore the bottom-up scaling allows to perform
preliminary mathematical analysis and write efficient numerical schemes. This
model is intended as a predictive tool for the investigation of bacterial
collective motion
On the fractional Fisher information with applications to a hyperbolic-parabolic system of chemotaxis
We introduce new lower bounds for the fractional Fisher information. Equipped
with these bounds we study a hyperbolic-parabolic model of chemotaxis and prove
the global existence of solutions in certain dissipation regimes
Mathematical description of bacterial traveling pulses
The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on E. coli have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with E. coli. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion