Related papers: Phase-field gradient theory
Geologic shear fractures such as faults and slip surfaces involve marked friction along the discontinuities as they are subjected to significant confining pressures. This friction plays a critical role in the growth of these shear…
The driven transport of plastic systems in various disordered backgrounds is studied within mean field theory. Plasticity is modeled using non-convex interparticle potentials that allow for phase slips. This theory most naturally describes…
In this continuum theory, we propose a mathematical framework to study the mechanical interplay of bulk-surfaces materials undergoing deformation and phase segregation. To this end, we devise a principle of virtual powers with a…
In this paper, a thermodynamically consistent phase-field model is proposed to describe the mass transport and reaction processes of multiple species in a fluid. A key feature of this model is that reactions between different species occur…
The phase-field crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field crystal dynamics can be…
We present a continuum theory to describe elastically induced phase transitions between coherent solid phases. In the limit of vanishing elastic constants in one of the phases, the model can be used to describe fracture on the basis of the…
We analyze a phase-field approximation of a sharp-interface model for two- phase materials proposed by M. Silhavy [32, 33]. The distinguishing trait of the model resides in the fact that the interfacial term is Eulerian in nature, for it is…
The structure of many multiphase systems is governed by an energy that penalizes the area of interfaces between phases weighted by surface tension coefficients. However, interface evolution laws depend also on interface mobility…
At high temperature and pressure, solid diffusion and chemical reactions between rock minerals lead to phase transformations. Chemical transport during uphill diffusion causes phase separation, that is, spinodal decomposition. Thus, to…
We develop an inhomogeneous mean-field theory for the extended Bose-Hubbard model with a quadratic, confining potential. In the absence of this potential, our mean-field theory yields the phase diagram of the homogeneous extended…
Aims: The test-field method for computing turbulent transport coefficients from simulations of hydromagnetic flows is extended to the regime with a magnetohydrodynamic (MHD) background. Methods: A generalized set of test equations is…
We extend a phase-field/gradient damage formulation for cohesive fracture to the dynamic case. The model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions.…
We derive rates of convergence for limit theorems that reveal the intricate structure of the phase transitions in a mean-field version of the Blume-Emery-Griffith model. The theorems consist of scaling limits for the total spin. The model…
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…
Phase field modelling offers an extremely general framework to predict microstructural evolutions in complex systems. However, its computational implementation requires a discretisation scheme with a grid spacing small enough to preserve…
Hybrid particle-field methods are computationally efficient approaches for modelling soft matter systems. So far applications of these methodologies have been limited to constant volume conditions. Here, we reformulate particle-field…
Using a regularized delta function to distribute surfactant interfacial concentration can simplify the computation of the surface gradient operator $\nabla_s$, enabling the phase-field model to effectively simulate Marangoni flows involving…
We propose a novel phase-field model to predict elastic microphase separation in polymer gels. To this end, we extend the Cahn-Hilliard free-energy functional to incorporate an elastic strain energy and a coupling term. These contributions…
The multi-phase-field approach is generalized to treat capillarity-driven diffusion parallel to the surfaces and phase-boundaries, i.e. the boundaries between a condensed phase and its vapor and the boundaries between two or multiple…
The analytical zero-temperature phase diagram of the double exchange model for classical background spins as a function of the carrier density and Hund's coupling in the entire range of these parameters is presented. By constructing a…