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The properties of the interface in a phase-separated solution of polymers with different degrees of polymerization and Kuhn segment lengths are calculated. The starting point is the planar interface, the profile of which is calculated in…
The work presents an integral solution of the time-fractional subdiffusion through a preliminary defined profile with unknown coefficients and the concept of penetration layer well known from the heat diffusion The profile satisfies the…
In three space dimensions, we consider the compressible inviscid model describing the time evolution of two fluids sharing the same velocity and enjoying the algebraic pressure closure. By employing the technique of convex integration, we…
Multiphase flows are characterized by sharp moving interfaces, separating different fluids or phases. In many cases the dynamics of the interface determines the behavior of the flow. In a coarse, or reduced order model, it may therefore be…
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…
We consider three models of evolving interfaces intimately related to the weakly asymmetric simple exclusion process with $N$ particles on a finite lattice of $2N$ sites. Our Model 1 defines an evolving bridge on $[0,1]$, our Model 1-w an…
High-accuracy, high-efficiency physics-based fluid-solid interaction is essential for reality modeling and computer animation in online games or real-time Virtual Reality (VR) systems. However, the large-scale simulation of incompressible…
Vision Transformers (ViT) have marked a paradigm shift in computer vision, outperforming state-of-the-art models across diverse tasks. However, their practical deployment is hampered by high computational and memory demands. This study…
We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…
In this paper, we introduce a diffuse interface model for describing the dynamics of mixtures involving multiple (two or more) phases. The coupled hydrodynamical system is derived through an energetic variational approach. The total energy…
We analyze a linear 3D/3D fluid-structure interaction problem between a thin layer of a viscous fluid and a thin elastic plate-like structure with the aim of deriving a simplified reduced model. Based on suitable energy dissipation…
We derive a reduced model of solute transport in blood based on the center manifold theory. The derivation is carried out on a convection diffusion equation with general axial and radial velocity profiles in a blood vessel of varying cross…
The capability to accurately predict flood flows via numerical simulations is a key component of contemporary flood risk management practice. However, modern flood models lack the capacity to accurately model flow interactions with linear…
Nonlocal models provide accurate representations of physical phenomena ranging from fracture mechanics to complex subsurface flows, where traditional partial differential equations fail to capture effects caused by long-range forces at the…
The variation of energies associated with soft matter interfaces where surface inhomogeneities are present. These energies include the total bending and splay energy, the variable surface tension energy, a coupling energy between the total…
In the self-consistent continuum solvation (SCCS) approach ($\textit{J. Chem. Phys.}$ 136, 064102 (2012)), the analytical expressions of the local solute-solvent interface functions determine the interface function and dielectric function…
Based on the thermodynamic variation, we rigorously derive the sharp-interface model for solid-state dewetting on a flat substrate in the form of cylindrical symmetry. The governing equations for the model belong to fourth-order geometric…
The expressiveness of flow-based models combined with stochastic variational inference (SVI) has expanded the application of optimization-based Bayesian inference to highly complex problems. However, despite the importance of multi-model…
The Immersed Interface Method is employed to solve the time-varying electric field equations around a three-dimensional vesicle. To achieve second-order accuracy the implicit jump conditions for the electric potential, up to the second…
We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…