相关论文: General neck condition for the limit shape of budd…

In this paper, we introduce and study the conformal mean curvature flow of submanifolds of higher codimension in the Euclidean space $\bbr^n$. This kind of flow is a special case of a general modified mean curvature flow which is of various…

Bubble formation and detachment at a submerged orifice exists widely in both daily life and academic research, and the influence of solid surface on bubble formation and detachment has also been extensively investigated. For example, it has…

Vesicle dynamics in unbounded Poiseuille flow is analyzed using a small-deformation theory. Our analytical results quantitatively describe vesicle migration and provide new physical insights. At low ratio between the inner and outer…

The geometry of rough, textured, fractured and porous media is topologically complicated. Those media are commonly represented by bundles of capillary tubes when modeled. However, angle-containing geometries can serve as a more realistic…

Viscous vortex layers subject to a more general uniform strain are considered. They include Townsend's steady solution for plane strain (corresponding to a parameter $a = 1$) in which all the strain in the plane of the layer goes toward…

Cellular internalization of nanoparticles requires the full wrapping of the nanoparticles by the cell membrane. This wrapping process can occur spontaneously if the adhesive interactions between the nanoparticles and the membranes are…

The growth, form, and division of prebiotic vesicles, membraneous bags of fluid of varying components and shapes is hypothesized to have served as the substrate for the origin of life. The dynamics of these out-of-equilibrium structures is…

We report an experimental and theoretical study of the global stability and nonlinear dynamics of vertical jets of viscous liquid confined in the axial direction due to their impact on a bath of the same liquid. Previous works demonstrated…

Engineering synthetic materials that mimic the remarkable complexity of living organisms is a fundamental challenge in science and technology. We study the spatiotemporal patterns that emerge when an active nematicfilm of microtubules and…

A two-dimensional or quasi-two-dimensional nematic liquid crystal refers to a surface confined system. When such a system is further confined by external line boundaries or excluded from internal line boundaries, the nematic directors form…

A spacelike surface S immersed in a 4-dimensional Lorentzian manifold will be said to be umbilical along a direction N normal to S if the second fundamental form along N is proportional to the first fundamental form of S. In particular, S…

Inspired by recent experiments that highlight the role of nematic defects in the morphogenesis of epithelial tissues, we develop a minimal framework to study the dynamics of an active curved surface driven by its nematic texture. Allowing…

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…

We study Brakke's mean curvature flow with obstacles and with a right-angle boundary condition. Assuming that the obstacles have $C^{1,1}$-boundaries we prove that a weak solution exists globally in time. To show the existence we apply the…

We investigate the topology and geometry of compact submanifolds in space forms of nonnegative curvature that satisfy a lower bound on the sectional curvature, depending only on the length of the mean curvature vector of the immersion. We…

In the first part of this paper, we develop the theory of anisotropic curvature measures for convex bodies in the Euclidean space. It is proved that any convex body whose boundary anisotropic curvature measure equals a linear combination of…

Morphologies of a vesicle confined in a spherical vesicle were explored experimentally by fast confocal laser microscopy and numerically by a dynamically-triangulated membrane model with area-difference elasticity. The confinement was found…

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…

Here we study the shapes of droplets captured between chemically distinct parallel plates. This work is a preliminary step toward characterizing the influence of second-phase bridging between biomolecular surfaces on their solution…

Biological membranes constantly change their shape in response to external stimuli, and understanding the remodeling and stability of vesicles in heterogeneous environments is therefore of fundamental importance for a range of cellular…