Related papers: Criteria of amorphous solidification
We study the long-time dynamics of hexagonal directional-solidification patterns in bulk samples of a transparent eutectic alloy using an optical method which permits real-time observation of the growth front. A slow dilatation of the…
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…
Surface incompressibility, also called inextensibility, imposes a zero-surface-divergence constraint on the velocity of a closed deformable material surface. The well-posedness of the mechanical problem under such constraint depends on an…
Fluid dynamics corresponds to the dynamics of a substance in the long wavelength limit. Writing down all terms in a gradient (long wavelength) expansion up to second order for a relativistic system at vanishing charge density, one obtains…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
In alloy solidification, the transport processes of heat and solute result in morphological instability of the interface, forming different patterns of solidification structure and determining the mechanical properties of components. As the…
We study the stability of amorphous solids, focusing on the distribution P(x) of the local stress increase x that would lead to an instability. We argue that this distribution is singular P(x)x^{\theta}, where the exponent {\theta} is…
We consider the growth of a vicinal crystal surface in the presence of a step-edge barrier. For any value of the barrier strength, measured by the length l_es, nucleation of islands on terraces is always able to destroy asymptotically…
We investigate the emergence of isotropic linear elasticity in amorphous and polycrystalline solids, via extensive numerical simulations. We show that the elastic properties are correlated over a finite length scale $\xi_E$, so that the…
The solidification of polycrystalline materials can be modelled by orientation-field models, which are formulated in terms of two continuous fields: a phase field that describes the thermodynamic state and an orientation field that…
The dynamics of steps on crystal surfaces is considered. In general, the meandering of the steps obeys a subdiffusive behaviour. The characteristic asymptotic time laws depend on the microscopic mechanism for detachment and attachment of…
We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in…
The problem of deriving a gradient flow structure for the porous medium equation which is {\em thermodynamic}, in that it arises from the large deviations of some microscopic particle system, is studied. To this end, a rescaled zero-range…
The universal anomalous vibrational and thermal properties of amorphous solids are believed to be related to the local variations of the elasticity. Recently it has been shown that the vibrational properties are sensitive to the glass's…
We study the problem of stabilization for the acoustic system with a spatially distributed damping. With imposing hypothesis on the structural properties of the damping term, we identify exponential decay of solutions with growing time.
Disclinations, first observed in mesomorphic phases, are relevant to a number of ill-ordered condensed matter media, with continuous symmetries or frustrated order. They also appear in polycrystals at the edges of grain boundaries. They are…
Surface growth is a crucial component of many natural and artificial processes from cell proliferation to additive manufacturing. In elastic systems surface growth is usually accompanied by the development of geometrical incompatibility…
We investigate the stability and geometrically non-linear dynamics of slender rods made of a linear isotropic poroelastic material. Dimensional reduction leads to the evolution equation for the shape of the poroelastica where, in addition…
We introduce and study the mechanical system which describes the dynamics and statics of rigid bodies of constant density floating in a calm incompressible fluid. Since much of the standard equilibrium theory, starting with Archimedes,…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…