Related papers: Softening of the Euler buckling criterion under di…
We extend slow manifolds near a transcritical singularity in a fast-slow system given by the explicit Euler discretization of the corresponding continuous-time normal form. The analysis uses the blow-up method and direct trajectory-based…
Euler turbulence has been experimentally observed to relax to a metaequilibrium state that does not maximize the Boltzmann entropy, but rather seems to minimize enstrophy. We show that a recent generalization of thermodynamics and…
An elastic double pendulum subject to a force acting along a fixed straight line, the so-called "Reut's column problem", is a structure exhibiting flutter and divergence instability, which was never realized in practice and thus debated…
We established the existence, uniqueness and stability of subsonic flows past an airfoil with a vortex line at the trailing edge. Such a flow pattern is governed by the two dimensional steady compressible Euler equations. The vortex line…
Entropy stabilization of the compressible Euler system is achieved by adapting the averages that are applied to the density and internal energy variables. The approach achieves non-linear robustness despite the use of simplified symmetric…
Carbon nanotubes tend to collapse when their diameters exceed a certain threshold, or when a sufficiently large external pressure is applied on their walls. Their radial stability of tubes has been studied in each of these cases, however a…
We evaluate the loss of stability of axially compressed slender and thick-walled tubes subject to a residual stress distribution. The nonlinear theory of elasticity, when used to analyze the underlying deformation, shows that the residual…
We rigorously justify the bilayer shallow-water system as an approximation to the hydrostatic Euler equations in situations where the flow is density-stratified with close-to-piecewise constant density profiles, and close-to-columnar…
The Stokes-Einstein-Sutherland (SES) equation is at the foundation of statistical physics, relating a particle's diffusion coefficient and size with the fluid viscosity, temperature and the boundary condition for the particle-solvent…
We use classical molecular dynamics simulations to study the collapse of single (SWNT) and double-walled (DWNT) carbon nanotube bundles under hydrostatic pressure. The collapse pressure (pc) varies as 1/R^3, where R is the SWNT radius or…
We investigate buckling of soft elastic capsules under negative pressure or for reduced capsule volume. Based on nonlinear shell theory and the assumption of a hyperelastic capsule membrane, shape equations for axisymmetric and initially…
We study the formation of singularity for the isothermal Euler-Poisson system arising from plasma physics. Contrast to the previous studies yielding only limited information on the blow-up solutions, for instance, sufficient conditions for…
The nonlinear mechanical response of carbon nanotubes, referred to as their "buckling" behavior, is a major topic in the nanotube research community. Buckling means a deformation process in which a large strain beyond a threshold causes an…
We are interested in the kernel of one-dimensional diffusion equations with continuous coefficients as evaluated by means of explicit discretization schemes of uniform step $h>0$ in the limit as $h\to0$. We consider both semidiscrete…
In recent work we have developed a renormalization framework for stabilizing reduced order models for time-dependent partial differential equations. We have applied this framework to the open problem of finite-time singularity formation…
In this article, we study the break-down of smooth and continuous solutions to isentropic Euler system in multi dimension. Sideris [Comm. Math. Phys. 1985] proved the blow up of smooth solutions when initial data satisfies an `integral…
The motion of a disk spinning to rest after being tipped on its side is a classic example of a finite-time singularity, yet the dominant dissipation mechanism governing this process remains debated. Using stereoscopic high-speed imaging, we…
The non-linear dynamics of driven oscillations in the size of a spherical bubble are mapped to the dynamics of a Newtonian particle in a potential within the incompressible liquid regime. The compressible liquid regime, which is important…
The fully-implicit time discretization (i.e. the backward Euler formula) is applied to compressible nonlinear dynamical models of viscoelastic solids in the Eulerian description, i.e. in the actual deforming configuration. The Kelvin-Voigt…
In some parameter and solution regimes, a minimally coupled nonrelativistic quantum particle in 1d is isomorphic to a much heavier, vibrating, very thin Euler-Bernoulli rod in 3d, with ratio of bending modulus to linear density…