Related papers: A continuum framework for phase field with bulk-su…
We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a mathematical model for the reaction between cell surface…
We consider the quantisation of scalar fields on a Lifshitz background, exploring the possibility of alternative boundary conditions, allowing the slow falloff mode to fluctuate. We show that the scalar field with alternative boundary…
The Cahn-Hilliard and viscous Cahn-Hilliard equations with singular and possibly nonsmooth potentials and dynamic boundary condition are considered and some well-posedness and regularity results are proved. Key words: Cahn-Hilliard…
In this paper, we study the longtime asymptotic behavior of a phase separation process occurring in a three-dimensional domain containing a fluid flow of given velocity. This process is modeled by a viscous convective Cahn-Hilliard system,…
The enforcement of global energy conservation in phase-field fracture simulations has been an open problem for the last 25 years. Specifically, the occurrence of unstable fracture is accompanied by a loss in total potential energy, which…
This work discusses the correct modeling of the fully nonlinear free surface boundary conditions to be prescribed in water waves flow simulations based on potential flow theory. The main goal of such a discussion is that of identifying a…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
Consider a model of particles (nucleons) which has a two-body interaction which leads to bound composites with saturation properties. These properties are : all composites have the same density and the ground state energies of composites…
The Cahn--Hilliard equation is one of the most common models to describe phase separation processes of a mixture of two materials. For a better description of short-range interactions between the material and the boundary, various dynamic…
A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. By rigorous asymptotic analysis we show that the sharp-interface limit of this model recovers the continuum model equations for the…
Liquid-gas phase coexistence in a boundary-driven diffusive system is studied by analyzing fluctuating hydrodynamics of a density field defined on a one-dimensional lattice with a space interval $\Lambda$. When an interface width $\ell$ is…
The Cahn-Hilliard equation is a fundamental model that describes the phase separation process in multi-component mixtures. It has been successfully extended to many different contexts in several scientific fields. In this survey article, we…
Phase field models have been applied in recent years to grain boundaries in single-component systems. The models are based on the minimization of a free energy functional, which is constructed phenomenologically rather than being derived…
The statistical mechanics of equilibrium interfaces has been well-established for over a half century. In the last decade, a wealth of observations have made increasingly clear that a new perspective is required to describe interfaces…
We consider a class of Cahn-Hilliard equation with kinetic rate dependent dynamic boundary conditions that describe possible short-range interactions between the binary mixture and the solid boundary. In the presence of surface diffusion on…
We consider non-linear evolution equations arising from mean-field limits of particle systems on discrete spaces. We investigate a notion of curvature bounds for these dynamics based on convexity of the free energy along interpolations in a…
Force fluctuations in granular materials are investigated. A continuum equation is derived starting from a discrete model proposed in the literature. The influence of boundary conditions is investigated. For periodic boundary conditions the…
Finite-size critical systems defined on a parallel plate geometry of finite extent along one single ($z$) direction with Dirichlet and Neumann boundary conditions at $z=0,L$ are analyzed in momentum space. We introduce a modified…
We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a…
The theory of point vortex dynamics has existed since Kirchhoff's proposal in 1891 and is still under development with connections to many fields in mathematics. As a strong simplification of the concept of vorticity it excels in…