Publications related to Initial value problem

Global existence for perturbations of the 2D stochastic Navier-Stokes equations with space-time white noise

We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations partial derivative( t)u + u center dot del u = Delta u - del p + sigma + xi, u(0, center dot ) = u(0),div (u) = 0, driven by additive space-time white noi ...

Springernature2024

Roughness Evolution Induced by Third-Body Wear

Jean-François Molinari, Tobias Brink, Antonio Joaquin Garcia Suarez

Surface roughness is a key factor when it comes to friction and wear, as well as to other physical properties. These phenomena are controlled by mechanisms acting at small scales, in which the topography of apparently flat surfaces is revealed. Roughness i ...

2024

Aerodynamic characterization of a delta-wing UAV based on real flight data

Jan Skaloud, Gabriel François Laupré, Pasquale Longobardi

Vehicle Dynamic Model based navigation represents a novel approach to autonomous navigation for small UAVs. It significantly improves the navigation solution under GNSS outage condition without adding additional sensors to the platform. This paper proposes ...

IEEE2021

Safe initialization of objects

Fengyun Liu

The inception of object-oriented programming introduces a category of bugs related to object construction: initialization errors. Every newly created object goes through several initialization states: starting from a state where all fields are uninitialize ...

EPFL2020

Modeling robot geometries like molecules, application to fast multi-contact posture planning for humanoids

Auke Ijspeert, Salman Faraji

Traditional joint-space models used to describe equations of motion for humanoid robots offer nice properties linked directly to the way these robots are built. However, from a computational point of view and convergence properties, these models are not th ...

Ieee-Inst Electrical Electronics Engineers Inc2018

Existence and Non-uniqueness of Global Weak Solutions to Inviscid Primitive and Boussinesq Equations

Elisabetta Chiodaroli

We consider the initial value problem for the inviscid Primitive and Boussinesq equations in three spatial dimensions. We recast both systems as an abstract Eulertype system and apply the methods of convex integration of De Lellis and Székelyhidi to show t ...

2017

The size of the sync basin revisited

Philippe René Joseph Jacquod, Robin Delabays

In dynamical systems, the full stability of fixed point solutions is determined by their basins of attraction. Characterizing the structure of these basins is, in general, a complicated task, especially in high dimensionality. Recent works have advocated t ...

American Institute of Physics2017

Location choice with longitudinal WiFi data

Michel Bierlaire, Matthieu Marie Cochon de Lapparent, Antonin Danalet, Loïc Tinguely

Location-aware data collection technologies provide new insights about location choices. Only a few dynamic models of location choice exist in scientific literature. To our knowledge, none of them correct for serial correlation. In this paper, we model cho ...

University of Leeds2016

Moment bounds and asymptotics for the stochastic wave equation

Robert Dalang, Le Chen

We consider the stochastic wave equation on the real line driven by space time white noise and with irregular initial data. We give bounds on higher moments and, for the hyperbolic Anderson model, explicit formulas for second moments. These bounds imply we ...

Elsevier Science Bv2015

Analytical approximations for the collapse of an empty spherical bubble

Mohamed Farhat, Danail Obreschkow

The Rayleigh equation 3/2 (R) over dot + R(R) double over dot + p rho(-1) = 0 with initial conditions R(0) = R-0, (R) over dot(0) = 0 models the collapse of an empty spherical bubble of radius R(T) in an ideal, infinite liquid with far-field pressure p and ...

2012

Global Solutions to a Non-Local Diffusion Equation with Quadratic Non-Linearity

Joachim Krieger

In this paper we prove the global in time well-posedness of the following non-local diffusion equation with

\alpha\, \varepsilon [0, 2/3)

:

\partial_tu=\{(-\Delta)^{-1}u\}\Delta u+\alpha u^2, \,\, u(t=0)=u_0

. The initial condition

u_0

is positive, rad ...

2012

The Bounded Confidence Model Of Opinion Dynamics

Jean-Yves Le Boudec, Javier Gomez Serrano

The bounded confidence model of opinion dynamics, introduced by Deffuant et al, is a stochastic model for the evolution of continuous-valued opinions within a finite group of peers. We prove that, as time goes to infinity, the opinions evolve globally into ...

World Scientific Publishing2012

A Globally Convergent Algorithm for the Run-to-Run Control of Systems with Sector Nonlinearities

Dominique Bonvin, Grégory François

Run-to-run control is a technique that exploits the repetitive nature of processes to iteratively adjust the inputs and drive the run-end outputs to their reference values. It can be used to control both static and finite-time dynamic systems. Although the ...

American Chemical Society2011

Nonlinear quasisteady state benchmark of global gyrokinetic codes

Laurent Villard, Stephan Brunner, Ben McMillan, Xavier Lapillonne

Two global gyrokinetic codes are benchmarked against each other by comparing simulation results in the case of ion temperature gradient driven turbulence, in the adiabatic electron response limit The two codes are the Eulerian code GENE and the Lagrangian ...

American Institute of Physics2010

Lectures on the Orbital Stability of Standing Waves and Application to the Nonlinear Schrodinger Equation

Charles Stuart

In the first part of these notes, we deal with first order Hamiltonian systems in the form Ju'(t) = del H(u(t)) where the phase space X may be in infinite dimensional so as to accommodate some partial differential equations. The Hamiltonian H is an element ...

Birkhäuser-Verlag, Springer2008

Steady-state Solutions in Mathematical Models of Atrial Cell Electrophysiology and their Stability

Vincent Jacquemet

The steady states of the Fenton–Karma, the Courtemanche and the Nygren cell models were studied by determining the fixed points of the dynamical system describing their cell kinetics. The linear stability of the fixed points was investigated, as well as th ...

2007