scholarly journals Touchdown is the Only Finite Time Singularity in a Three-Dimensional MEMS Model

2020 ◽  
Vol 27 (1) ◽  
pp. 65-81
Author(s):  
Philippe Laurençot ◽  
Christoph Walker
Keyword(s):  
Finite Time ◽  
Three Dimensional ◽  
Time Singularity ◽  
Finite Time Singularity

scholarly journals Optimal renormalization of multiscale systems

2021 ◽  
Vol 118 (37) ◽  
pp. e2102266118
Author(s):  
Jacob Price ◽  
Brek Meuris ◽  
Madelyn Shapiro ◽  
Panos Stinis
Keyword(s):  
Finite Time ◽  
Three Dimensional ◽  
Order Reduction ◽  
Time Dependent ◽  
Reduced Order Models ◽  
Time Decay ◽  
Time Singularity ◽  
Reduced Order ◽  
Renormalization Approach ◽  
Finite Time Singularity

While model order reduction is a promising approach in dealing with multiscale time-dependent systems that are too large or too expensive to simulate for long times, the resulting reduced order models can suffer from instabilities. We have recently developed a time-dependent renormalization approach to stabilize such reduced models. In the current work, we extend this framework by introducing a parameter that controls the time decay of the memory of such models and optimally select this parameter based on limited fully resolved simulations. First, we demonstrate our framework on the inviscid Burgers equation whose solution develops a finite-time singularity. Our renormalized reduced order models are stable and accurate for long times while using for their calibration only data from a full order simulation before the occurrence of the singularity. Furthermore, we apply this framework to the three-dimensional (3D) Euler equations of incompressible fluid flow, where the problem of finite-time singularity formation is still open and where brute force simulation is only feasible for short times. Our approach allows us to obtain a perturbatively renormalizable model which is stable for long times and includes all the complex effects present in the 3D Euler dynamics. We find that, in each application, the renormalization coefficients display algebraic decay with increasing resolution and that the parameter which controls the time decay of the memory is problem-dependent.

scholarly journals Finite-time singularity versus global regularity for hyper-viscous Hamilton–Jacobi-like equations

Nonlinearity ◽  
2003 ◽  
Vol 16 (6) ◽  
pp. 1967-1989 ◽  
Author(s):  
Hamid Bellout ◽  
Said Benachour ◽  
Edriss S Titi
Keyword(s):  
Finite Time ◽  
Global Regularity ◽  
Time Singularity ◽  
Finite Time Singularity

scholarly journals Interacting vacuum at infinity

2019 ◽  
Vol 16 (04) ◽  
pp. 1950052
Author(s):  
G. Kittou
Keyword(s):  
Finite Time ◽  
Central Extension ◽  
Vacuum Model ◽  
Time Singularity ◽  
Attractor Solution ◽  
The One ◽  
Finite Time Singularity

We apply the central extension technique of Poincaré to dynamics involving an interacting mixture of pressureless matter and vacuum near a finite-time singularity. We show that the only attractor solution on the circle of infinity is the one describing a vanishing matter-vacuum model at early times.

Sign in / Sign up

Export Citation Format

Share Document