Related papers: On a phase field model for RNA-Protein dynamics

Second-order phase field models have emerged as an attractive option for capturing the advection of interfaces in two-phase flows. Prior to these, state-of-the-art models based on the Cahn-Hilliard equation, which is a fourth-order…

The motion of microstructural interfaces is important in modeling materials that undergo twinning and structural phase transformations. Continuum models fall into two classes: sharp-interface models, where interfaces are singular surfaces;…

We study genetic networks that produce many species of non-coding RNA molecules that are present at a moderate density, as typically exists in the cell. The associations of the many species of these RNA are modeled physically, taking into…

A theoretical framework is developed to study the dynamics of protein folding. The key insight is that the search for the native protein conformation is influenced by the rate r at which external parameters, such as temperature, chemical…

In this paper we study a non-local Cahn-Hilliard equation with singular single-well potential and degenerate mobility. This results as a particular case of a more general model derived for a binary, saturated, closed and incompressible…

We show short-time well-posedness of a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including…

In this paper, the authors study the distributed optimal control of a system of three evolutionary equations involving fractional powers of three selfadjoint, monotone, unbounded linear operators having compact resolvents. The system is a…

We present a long-wavelength approximation to the Navier-Stokes Cahn-Hilliard equations to describe phase separation in thin films. The equations we derive underscore the coupled behaviour of free-surface variations and phase separation.…

In this paper we devise and analyze an unconditionally stable, second-order-in-time numerical scheme for the Cahn-Hilliard equation in two and three space dimensions. We prove that our two-step scheme is unconditionally energy stable and…

Many systems exhibit a phase where the order parameter is spatially modulated. These patterns can be the result of a frustration caused by the competition between interaction forces with opposite effects. In all models with local…

During phase transitions certain properties of a material change, such as composition field and lattice-symmetry distortions. These changes are typically coupled, and affect the microstructures that form in materials. Here, we propose a 2D…

A class of models of driven diffusive systems which is shown to exhibit phase separation in $d=1$ dimensions is introduced. Unlike all previously studied models exhibiting similar phenomena, here the phase separated state is fluctuating in…

We review how phase-field models contributed to the understanding of various aspects of crystal nucleation including homogeneous and heterogeneous processes, and their role in microstructure evolution. We recall results obtained both by the…

DNA is now firmly established as a versatile and robust platform for achieving synthetic nanostructures. While the folding of single molecules into complex structures is routinely achieved through engineering basepair sequences, much less…

The kinetic folding of RNA sequences into secondary structures is modeled as a complex adaptive system, the components of which are possible RNA structural rearrangements (SRs) and their associated bases and base pairs. RNA bases and base…

In this work, we investigate a distributed optimal control problem for an extended phase field system of Cahn--Hilliard type which physical context is that of tumor growth dynamics. In a previous contribution, the author has already studied…

We focus on the derivation and analysis of a model for multi-component phase separation occurring on biological membranes, inspired by observations of lipid raft formation. The model integrates local membrane composition with local membrane…

The phase transition patterns displayed by a model of two coupled complex scalar fields are studied at finite temperature and chemical potential. Possible phenomena like symmetry persistence and inverse symmetry breaking at high…

We study a non-local version of the Cahn-Hilliard dynamics for phase separation in a two-component incompressible and immiscible mixture with linear mobilities. In difference to the celebrated local model with nonlinear mobility, it is only…

We propose an active Cahn-Hilliard theory for the dynamics of a new type of phase transition where the driving force is not the direct interactions between the two separating components, but their active sorting by a third polar species.…