Related papers: Hexagonal eutectic solidification patterns operati…
In this paper the statement of the second Bogolyubov's theorem on periodic solutions of smooth systems with small parameter is justified for discountinuous systems. It is assumed that the generating solution intersects the discontinuity…
We consider the Taylor-Couette problem in an infinitely extended cylindrical domain. There exist modulated front solutions which describe the spreading of the stable Taylor vortices into the region of the unstable Couette flow. These…
We derive a compatible discretization method that relies heavily on the underlying geometric structure, and obeys the topological sequences and commuting properties that are constructed. As a sample problem we consider the…
We explore models of hard-rod fluids with a finite number of allowed orientations, and construct their bulk phase diagrams within Onsager's second virial theory. For a one-component fluid, we show that the discretization of the orientations…
We report a surface instability observed during the extrusion of extremely soft elastic solids in confined geometries. Due to their unique rheological properties, these soft solids can migrate through narrow gaps by continuously everting…
The mechanical response of isotropic elastoplastic materials containing random distributions of initially spherical voids is investigated computationally based on Fast Fourier Transform simulations. Numerical limit-analysis simulations at…
We study numerically and analytically the instabilities associated with phase separation in a solid layer on which an external material ux is imposed. The first instability is localized within a boundary layer at the exposed free surface by…
Hamiltonian dynamics of a thin vortex filament in ideal incompressible fluid near a flat fixed boundary is considered at the conditions that at any point of the curve determining shape of the filament the angle between tangent vector and…
We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element…
It is generally understood that geometric frustration prevents maximal hexagonal packings in uniform filament bundles upon twist. We demonstrate that a hexagonal packed elastic filament bundle can preserve its order over a wide range of…
The behavior of shear-oscillated amorphous materials is studied using a coarse-grained model. Samples are prepared at different degrees of annealing and then subject to athermal and quasistatic oscillatory deformations at various fixed…
Whether or not there is growing static order accompanying the dynamical heterogeneity and increasing relaxation times seen in glassy systems is a matter of dispute. An obstacle to resolving this issue is that the order is expected to be…
We consider surface-tension driven convection in a rotating fluid layer. For nearly insulating boundary conditions we derive a long-wave equation for the convection planform. Using a Galerkin method and direct numerical simulations we study…
We present a new analytic study of the equilibrium and stability properties of close binary systems containing polytropic components. Our method is based on the use of ellipsoidal trial functions in an energy variational principle. We…
Using molecular dynamics simulation, we study structural and dynamical heterogeneities at melting in two-dimensional one-component systems with 36000 particles. Between crystal and liquid we find intermediate hexatic states, where the…
The parameters in the governing system of partial differential equations of multicompartmental poroelastic models typically vary over several orders of magnitude making its stable discretization and efficient solution a challenging task. In…
The phase-ordering kinetics of a bulk uniaxial nematic liquid crystal is addressed using techniques that have been successfully applied to describe ordering in the O(n) model. The method involves constructing an appropriate mapping between…
Directional solidification of water-based solutions has emerged as a versatile technique to template hierarchical porous materials, but this nonequilibrium process remains incompletely understood. Here we use phase-field simulations to shed…
Exponential dichotomies play a central role in stability theory for dynamical systems. They allow to split the state space into two subspaces, where all trajectories in one subspace decay whereas all trajectories in the other subspace grow,…
We present adaptive finite element simulations of dendritic and eutectic solidification in binary and ternary alloys. The computations are based on a recently formulated phase-field model that is especially appropriate for modelling…