Related papers: Convergence of Phase-Field Free Energy and Boundar…
An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn-Hilliard type is carried out as the coefficient of the surface diffusion acting on the phase variable tends to 0, thus obtaining a forward-backward…
Reproducing the key features of fracture behavior under multiaxial stress states is essential for accurate modeling. Experimental evidence indicates that three intrinsic material properties govern fracture nucleation in elastic materials:…
A system with equation and dynamic boundary condition of Cahn-Hilliard type is considered. This system comes from a derivation performed in Liu-Wu (Arch. Ration. Mech. Anal. 233 (2019), 167--247) via an energetic variational approach.…
We generalize Wheeler-Feynman electrodynamics by the minimization of a finite action functional defined for variational trajectories that are required to merge continuously into given past and future boundary segments. We prove that the…
Self-consistent calculations of the energy-loss spectra of charged particles moving near a plane-bounded free electron gas are reported. Energy-loss probabilities are obtained, within linear-response theory, from the knowledge of the…
The standard model for diffuse charge phenomena in colloid science, electrokinetics and biology is the Poisson-Boltzmann mean-field theory, which breaks down for multivalent ions and large surface charge densities due to electrostatic…
We derive the interfacial tension of a semi infinite two phase binary mixture of partially miscible fluids in contact with a planar surface. In our model we take a surface free energy term into account omitted by Cahn [J. W. Cahn, J.…
Using techniques of complex analysis in an algebraic approach, we solve the wave equation for a two-level atom interacting with a monochromatic light field exactly. A closed-form expression for the quasi-energies is obtained, which shows…
The ab-initio computational treatment of electrochemical systems requires an appropriate treatment of the solid/liquid interfaces. A fully quantum mechanical treatment of the interface is computationally demanding due to the large number of…
In this paper an iterative minimization method is proposed to approximate the minimizer to the double-well energy functional arising in the phase-field theory. The method is based on a quadratic functional posed over a nonempty closed…
We present a new multiphase-field theory for describing pattern formation in multi-domain and/or multi-component systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure mathematical…
We consider a diffuse-interface model for two-phase incompressible viscous flows with a soluble surfactant in a bounded porous medium. This hydrodynamic system consists of a Darcy--Forchheimer equation for the seepage velocity…
This paper is devoted to the numerical study of droplet impact on solid substrates in presence of surfactants. We formulate the problem in an energetically variational framework and introduce an incompressible Cahn-Hilliard-Navier-Stokes…
Classical descriptions of flapping propulsion near a free surface emphasize the energetic penalties of wave generation, treating the interface primarily as an energy sink. Here, we show that the same deformable boundary can also act as a…
Jarzynski's equality [1] allows us to investigate free energy landscapes (FELs) by constructing distributions of work performed on a system from an initial ensemble of states to final states. This work is experimentally measured by…
In this paper, we introduce a model describing the dynamic of vesicle membranes within an incompressible viscous fluid in $3D$ domains. The system consists of the Navier-Stokes equations, with an extra stress tensor depending on the…
The Cahn-Hilliard equation has a wide range of applications in many areas of physics and chemistry. To describe the short-range interaction between the solution and the boundary, scientists have constructed dynamical boundary conditions by…
We have observed momentum- and position-resolved spectra and images of the photoluminescence from thermalised and condensed dye-microcavity photons. The spectra yield the dispersion relation and the potential energy landscape for the…
Room temperature ionic liquids are attractive to numerous applications and particularly, to renewable energy devices. As solvent free electrolytes, they demonstrate a paramount connection between the material morphology and Coulombic…
Energy levels are investigated for two charged particles possessing an attractive, momentum-independent, zero-range interaction in a uniform magnetic field. A transcendental equation governs the spectrum, which is characterized by a…