Related papers: Existence, uniqueness, and energy scaling of 2+1 d…
Step meandering due to a deterministic morphological instability on vicinal surfaces during growth is studied. We investigate nonlinear dynamics of a step model with asymmetric step kinetics, terrace and line diffusion, by means of a…
Quasistatic evolutions of critical points of time-dependent energies exhibit piecewise smooth behavior, making them useful for modeling continuum mechanics phenomena like elastic-plasticity and fracture. Traditionally, such evolutions have…
We use a one-dimensional step model to study quantitatively the growth of step bunches on Si(111) surfaces induced by a direct heating current. Parameters in the model are fixed from experimental measurements near 900 deg C under the…
Since the celebrated paper by El Karoui, Peng and Quenez [Mathematical Finance, 7 (1997), 1--71], backward stochastic differential equations have found wide applications in stochastic control, financial technology and machine learning. In…
There are conflicting reports in the literature regarding the finite-size scaling of the Liouvillian gap and dynamical fluctuations at discontinuous phase transitions, with various studies reporting either exponential or power-law behavior.…
Some dynamical properties of non interacting particles in a bouncer model are described. They move under gravity experiencing collisions with a moving platform. The evolution to steady state is described in two cases for dissipative…
Step meandering instability in a Burton-Cabrera-Frank (BCF)-type model for the growth of an isolated, atomically high step on a crystal surface is analyzed. It is assumed that the growth is sustained by the molecular precursors deposition…
A continuum growth equation in 1+1 dimensions is obtained by considering the contributions to the underlying current from kinetics of adatoms on the surface. These considerations reproduce the slope dependent term that represents a stable…
We introduce a new equation describing epitaxial growth processes. This equation is derived from a simple variational geometric principle and it has a straightforward interpretation in terms of continuum and microscopic physics. It is also…
We revisit the velocity-dependent one-scale model for topological defect evolution, and present a new alternative formulation in terms of a physical (rather than invariant) characteristic length scale. While the two approaches are…
This work rigorously implements a recent model of large-strain elasto-plastic evolution in single crystals where the plastic flow is driven by the movement of discrete dislocation lines. The model is geometrically and elastically nonlinear,…
The behavior of a surface energy $\mathcal F(E,u)$, where $E$ is a set of finite perimeter and $u\in L^1(\partial^* E, \mathbb R_+)$ is studied. These energies have been recently considered in the context of materials science to derive a…
We analyze in detail the Solid-On-Solid model (SOS) for growth processes on a square substrate in 2+1 dimensions. By using the Markovian surface properties, we introduce an alternative approach for determining the roughness exponent of a…
We study a dissipative system of nonlinear and nonlocal equations modeling the flow of electrohydrodynamics. The existence, uniqueness and regularity of solutions is proven for general $\mathbf{L}^2$ initial data in two space dimensions and…
A class of nonequilibrium models with short-range interactions and sequential updates is presented. The models describe one dimensional growth processes which display a roughening transition between a smooth and a rough phase. This…
We develop a global wellposedness theory for weak solutions to the 1D Euler-alignment system with measure-valued density, bounded velocity, and locally integrable communication protocol. A satisfactory understanding of the low-regularity…
We propose a novel approach to continuum modelling of dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual…
A finite temperature version of body-centered solid-on-solid growth models involving attachment and detachment of dimers is discussed in 1+1 dimensions. The dynamic exponent of the growing interface is studied numerically via the spectrum…
The quasistatic approximation is a useful but questionable simplification for analyzing step instabilities during the growth/evaporation of vicinal surfaces. Using this approximation, we characterized in Part I of this work the effect on…
In this paper we review a series of results obtained for 1D and 2D simple N-body dynamical models with infinite-range attractive interactions and without short distance singularities. The free energy of both models can be exactly obtained…