Related papers: Phase field approach for modeling intracellular dy…
Evolving from turbulent states the 2D fluids and the plasmas reach states characterized by a high degree of order, consisting of few vortices. These asymptotic states represent a small subset in the space of functions and are characterised…
Automated cell segmentation in microscopy images is essential for biomedical research, yet conventional methods are labor-intensive and prone to error. While deep learning-based approaches have proven effective, they often require large…
We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the…
The phase diagram of a lattice microemulsion model proposed by Ciach, H{\o}ye and Stell is studied using mean-field theory and Monte Carlo simulations. Surfactant directional degrees of freedom are summed out exactly before mean-field…
We derive a novel efficient scheme to measure the rate constant of transitions between stable states separated by high free energy barriers in a complex environment within the framework of transition path sampling. The method is based on…
This paper proposes a phase field model (PFM) for describing hydraulic fracture propagation in transversely isotopic media. The coupling between the fluid flow and displacement fields is established according to the classical Biot…
Confluent cell monolayers and epithelia tissues show remarkable patterns and correlations in structural arrangements and actively-driven collective flows. We simulate these properties using multiphase field models. The models are based on…
We introduce a simulation strategy to consistently couple continuum biomembrane dynamics to the motion of discrete biological macromolecules residing within or on the membrane. The methodology is used to study the diffusion of integral…
Nowadays, harmful effects of climate change are becoming increasingly apparent. A vital issue that must be addressed is the generation of energy from non-renewable and often polluting sources. For this reason, the development of renewable…
The investigation of tumor invasion and metastasis dynamics is crucial for advancements in cancer biology and treatment. Many mathematical models have been developed to study the invasion of host tissue by tumor cells. In this paper, we…
A phase-field crystal model based on the density-field approach incorporating high-order interparticle direct correlations is developed to study vapor-liquid-solid coexistence and transitions within a single continuum description.…
We introduce a continuous modeling approach which combines elastic responds of the trabecular bone structure, the concentration of signaling molecules within the bone and a mechanism how this concentration at the bone surface is used for…
A phase-field formulation is introduced to simulate quantitatively microstructural pattern formation in alloys. The thin-interface limit of this formulation yields a much less stringent restriction on the choice of interface thickness than…
A phase diagram, defined by the amplitude square and phase of scattering coefficients for absorption cross-section in each individual channel, is introduced as a universal map on the electromagnetic properties for passive scatterers.…
Phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems. Here, we develop a new analytical approach based on bifurcation analysis to explore…
An existence result is proved for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial conditions.…
Thermofield dynamics has proven to be a very useful theory in high-energy physics, particularly since it permits the treatment of both time- and temperature-dependence on an equal footing. We here show that it also has an excellent…
A modified phase field crystal model in which the free energy may be minimised by an order parameter profile having isolated bumps is investigated. The phase diagram is calculated in one and two dimensions and we locate the regions where…
We present a general framework to model spontaneous emission in integrated photonic structures by exploiting quantization of the electromagnetic field in terms of asymptotic in/out modes. This approach allows for an efficient and physically…
A phase field model with two phase fields, representing the concentration and the head-tail separation of amphiphilic molecules, respectively, has been constructed using an extension of the Ohta-Kawasaki model (Macromolecules 19, 2621-2632…