Related papers: A vector equilibrium problem for symmetrically loc…
We present a solvable model inspired by dimensional analysis for the time-dependent spreading of droplets that partially wet a substrate, where the spreading eventually stops and the contact angle reaches a nonzero equilibrium value. We…
The numerical approximation of 2D elasticity problems is considered, in the framework of the small strain theory and in connection with the mixed Hellinger-Reissner variational formulation. A low-order Virtual Element Method (VEM) with…
We present a Virtual Element Method (VEM) for the solution of Dirichlet problems for the quasilinear equation $-\text{div} (k(u)\text{grad} u)=f$ with essential boundary conditions. Within the VEM the nonlinear coefficient is evaluated with…
Results from the state-of-the-art molecular dynamics simulations are presented for both equilibrium and nonequilibrium dynamics following vapor-liquid transition in a single component Lennard-Jones system. We have fixed the overall density…
A classical model of fluid dynamics is considered which describes the shape evolution of a viscous liquid droplet on a homogeneous substrate. All equilibria are characterized and their stability is analyzed by a geometric reduction…
We study the logarithmic equilibrium problem on the interval $[-1,1]$ in the presence of an external field generated by a uniform background charge supported on the same interval. For a real parameter $\tau$, the external field is taken to…
We study the interaction of a liquid drop with an elastic beam in the case where bending effects dominate. We use a variational approach to derive equilibrium equations for the system in the presence of gravity and in the presence or…
We investigate the relationship between rigid motions and relative equilibria in the N-body problem on the two-dimensional sphere, S2. We prove that any rigid motion of the N-body system on S2 must be a relative equilibrium. Our approach…
An exact description is provided of an almost spherical fluid vesicle with a fixed area and a fixed enclosed volume locally deformed by external normal forces bringing two nearby points on the surface together symmetrically. The conformal…
Due to the potential application of regulating droplet shape by external fields in microfluidic technology and micro devices, it becomes increasingly important to understand the shape formation of a droplet in the presence of an electric…
The problem of the equilibrium state of the charged many-particle system above dielectric surface is formulated.We consider the case of the presence of the external attractive pressing field and the case of its absence. The equilibrium…
We consider a classical (capillary) model for a one-phase liquid in equilibrium. The liquid (e.g. water) is subject to a volume constraint, it does not mix with the surrounding vapour (e.g. air), it may come into contact with solid supports…
An example of capillary phenomena commonly seen and often studied is a droplet of water hanging in air from a horizontal surface. A thin capillary surface interface between the liquid and gas develops tangential surface tension, which…
We theoretically investigate the nucleation of liquid droplets from vapor in the presence of a charged spherical particle. Due to field gradients, sufficiently close to the critical point of the vapor--gas system, the charge destabilizes…
In the present paper we introduce a Virtual Element Method (VEM) for the approximate solution of general linear second order elliptic problems in mixed form, allowing for variable coefficients. We derive a theoretical convergence analysis…
The Virtual Element Method (VEM) is a well-established framework for solving partial differential equations on polygonal and polyhedral meshes. In this paper, we introduce a novel hybrid VEM that integrates both conforming and nonconforming…
In this note we study a minimization problem for a vector of measures subject to a prescribed interaction matrix in the presence of external potentials. The conductors are allowed to have zero distance from each other but the external…
We consider the minimal energy problem on the unit sphere $\mathbb S^2$ in the Euclidean space $\mathbb R^3$ immersed in an external field $Q$, where the charges are assumed to interact via Newtonian potential $1/r$, $r$ being the Euclidean…
We study a family of approximations to Euler's equation depending on two parameters $\varepsilon,\eta \ge 0$. When $\varepsilon=\eta=0$ we have Euler's equation and when both are positive we have instances of the class of…
We study the equilibrium measure for a logarithmic potential in the presence of an external field V*(x) + tp(x), where t is a parameter, V*(x) is a smooth function and p(x) a monic polynomial. When p(x) is of an odd degree, the equilibrium…