Related papers: Grain Boundary Grooving in a Bicrystal with Passiv…
We study the surface wrinkling of a stiff thin elastic film bonded to a compliant graded elastic substrate subject to compressive stress generated either by compression or growth of the bilayer. Our aim is to clarify the influence of the…
We have revealed the decisive role of grain-boundary-induced strain fields in electron scattering in polycrystalline graphene. To this end, we have formulated the model based on Boltzmann transport theory which properly takes into account…
The grain boundary (GB) microstructure influences and is influenced by the development of residual stresses during synthesis of polycrystalline thin films. Recent studies have shown that the frustration between the preferred growth…
We report the experimental demonstration of modulation instability process assisted by a dispersion grating in an optical fiber. A simple analytical model is developed to further analyze and explain the complex dynamics of this process,…
The equation arising from Prandtl boundary layer theory is considered. The existence of the entropy solution can be proved by BV estimate method. The interesting problem is that, since a may be degenerate on the boundary, the usual boundary…
The complex arrangements of atoms near grain boundaries are difficult to understand theoretically. We propose a phenomenological (Ginzburg-Landau-like) description of crystalline phases based on symmetries and fairly general stability…
We study the dynamics of a degenerate parabolic equation with a variable, generally non-smooth diffusion coefficient, which may vanish at some points or be unbounded. We show the existence of a global branch of nonnegative stationary…
We consider the roughening of small angle grain boundaries consisting of arrays of dislocations and found two transitions, corresponding to fluctuations of the dislocations along and perpendicular to the boundaries. The latter contributes…
We consider surfaces with boundary satisfying a sixth order nonlinear elliptic partial differential equation corresponding to extremising the $L^2$-norm of the gradient of the mean curvature. We show that such surfaces with small $L^2$-norm…
Thermal stability of nanocrystalline multilayer thin film is of paramount importance as the applications often involve high temperature. Here we report on the layer instability phenomenon in binary polycrystalline thin film initiating from…
It was recently reported that segregation of Zr to grain boundaries (GB) in nanocrystalline Cu can lead to the formation of disordered intergranular films [1,2]. In this study we employ atomistic computer simulations to study how the…
Grain boundaries affect properties of polycrystalline materials. The influence of a boundary is largely determined by its energy. Grain boundary energy is often portrayed as a function of macroscopic boundary parameters representing grain…
Sixth-order boundary value problems (BVPs) arise in thin-film flows with a surface that has elastic bending resistance. We consider the case in which the elastic interface is clamped at the lateral walls of a closed trough and thus encloses…
Grain boundaries play a critical role in applications of superconducting Nb$_3$Sn: in dc applications, grain boundaries preserve the material's inherently high critical current density by pinning flux, while in ac applications grain…
An expression for the stress tensor near an external boundary of a discrete mechanical system is derived explicitly in terms of the constituents' degrees of freedom and interaction forces. Starting point is the exact and general coarse…
We investigate analytically and numerically the interaction between grain boundaries and second phase precipitates in two-phase coherent solids in the presence of misfit strain. Our numerical study uses amplitude equations that describe the…
A linear sixth-order partial differential equation (PDE) of ``parabolic'' type describes the dynamics of thin liquid films beneath surfaces with elastic bending resistance when deflections from the equilibrium film height are small. On a…
A finite-deformation framework for gradient crystal plasticity is developed within a thermodynamically consistent setting grounded in Gurtin's power-conjugate formulation. The model introduces a flow rule that accounts explicitly for both…
Two main existence theorems are proved for two nonstandard systems of parabolic initial-boundary value problems. The systems are based on the "$ \phi $-$ \eta $-$ \theta $ model" proposed by Kobayashi [RIMS Kokyuroku, 1210 (2001), 68-77] as…
In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A function that has a prescribed value on the domain in which a differential…