Related papers: Crystal dislocations with different orientations a…
We consider a strongly nonlinear PDE system describing solid-solid phase transitions in shape memory alloys. The system accounts for the evolution of an order parameter (related to different symmetries of the crystal lattice in the phase…
Freestanding tubular crystals offer a general description of crystalline order on deformable surfaces with cylindrical topology, such as single-walled carbon nanotubes, microtubules, and recently reported colloidal assemblies. These systems…
With using of point-dipole model the theoretical calculations of main refractive indices and orientation of indicatrix of 18 minerals are performed. The feature of studied minerals is the statistically disordered arrangement of CO3, SO4,…
The motion of topological defects is an important feature of the dynamics of all liquid crystals, and is especially conspicuous in active liquid crystals. Understanding defect motion is a challenging theoretical problem, because the…
Structural response of crystals to an applied external perturbation is important as a key for understanding microscopic origin of physical properties. Experimental investigation of structural response is a great challenge for modern…
Finding an optimal match between two different crystal structures underpins many important materials science problems, including describing solid-solid phase transitions, developing models for interface and grain boundary structures. In…
We derive parametric travelling-wave solutions of non-linear QCD equations. They describe the evolution towards saturation in the geometric scaling region. The method, based on an expansion in the inverse of the wave velocity, leads to a…
We report a numerical study of the rate of crystal nucleation in a binary suspension of oppositely charged colloids. Two different crystal structures compete in the thermodynamic conditions under study. We find that the crystal phase that…
As circuitry approaches single nanometer length scales, it is important to predict the stability of metals at these scales. The behavior of metals at larger scales can be predicted based on the behavior of dislocations, but it is unclear if…
The time-dependent electromagnetic field can results both pair waves and pair particles. It can be for mathematical relations between two functions with identical argument and difference of phases equal to $\pi$. Two examples both the…
Consider the (simplified) Leslie-Erickson model for the flow of nematic liquid crystals in a bounded domain $\Omega \subset \mathbb{R}^n$ for n > 1$. This article develops a complete dynamic theory for these equations, analyzing the system…
This paper examines a system of partial differential equations describing dislocation dynamics in a crystalline solid. In particular we consider dynamics linearized about a state of zero stress and use linear semigroup theory to establish…
A theoretical framework is proposed to derive a dynamic equation motion for rectilinear dislocations within isotropic continuum elastodynamics. The theory relies on a recent dynamic extension of the Peierls-Nabarro equation, so as to…
We study some non-parabolic diffusion problems in one-space dimension, where the diffusion flux exhibits forward and backward nature of the Perona-Malik, H\"ollig or non-Fourier type. Classical weak solutions to such problems are…
It was recently shown that to predict reliable Peierls stresses from atomistic simulations, one has to correct the Peierls barrier by the zero-point energy difference between the initial and activated states of the dislocation. The…
In the continuum limit, the theory of dislocations in crystals predicts a divergence in the elastic energy of the host material at a crystal geometry dependent limiting (or critical) velocity $v_c$. Explicit expressions for $v_c$ are…
Life on Earth depends upon the dissolution of ionic salts in water, particularly NaCl. However, an atomistic scale understanding of the process remains elusive. Simulations lend themselves conveniently to studying dissolution since they…
Dislocations, line defects in crystalline materials, play an essential role in the mechanical[1,2], electrical[3], optical[4], thermal[5], and phase transition[6] properties of these materials. Dislocation motion, an important mechanism…
It is demonstrated by analyzing real examples that phase transitions in layered crystals occur like all other solid-state phase transitions by nucleation and crystal growth, but have a specific morphology. There the nucleation is epitaxial,…
Metals with fcc structure may exhibit deformation twinning under specific conditions, which is an interesting but somewhat elusive aspect of their deformation behavior. It is well acknowledged that the phenomenon occurs through the…