Related papers: Radius evolution for bubbles with elastic shells
On the basis of the two-fluid hydrodynamics, an analogue of the famous Rayleigh-Plesse equation for the dynamics of a spherical bubble in superfluid helium is obtained. The mass flow velocity $v$ and the velocity of the normal component…
The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of…
The dynamics of a membrane is a coupled system comprising a moving elastic surface and an incompressible membrane fluid. We will consider a reduced elastic surface model, which involves the evolution equations of the moving surface, the…
We preset a computational study of bending models for the curvature elasticity of lipid bilayer membranes that are relevant for simulations of vesicles and red blood cells. We compute bending energy and forces on triangulated meshes and…
Cellular membranes are elastic lipid bilayers that contain a variety of proteins, including ion channels, receptors, and scaffolding proteins. These proteins are known to diffuse in the plane of the membrane and to influence the bending of…
We present a general theory for the equilibrium structure of cylindrical tubules and helical ribbons of chiral lipid membranes. This theory is based on a continuum elastic free energy that permits variations in the direction of molecular…
Shape transformations of flat bilayer membranes and vesicles induced by hydrolysis and condensation reactions of amphiphilic molecules are studied using coarse-grained molecular dynamics simulations. The hydrolysis and condensation…
Motivated by the buckling of glassy crusts formed on evaporating droplets of polymer and colloid solutions, we numerically model the deformation and buckling of spherical elastic caps controlled by varying the volume between the shell and…
Directed Percolation (DP) is a classic model for nonequilibrium phase transitions into a single absorbing state (fixation). It has been extensively studied by analytical and numerical techniques in diverse contexts. Recently, DP has…
Within the framework of the well-known curvature models, a fluid lipid bilayer membrane is regarded as a surface embedded in the three-dimensional Euclidean space whose equilibrium shapes are described in terms of its mean and Gaussian…
In the core accretion model of planet formation, envelope cooling regulates the accretion of material and ultimately sets the timescale to form a giant planet. Given the diversity of planet-forming environments, opacity uncertainties, and…
The transport of particles across lipid-bilayer membranes is important for biological cells to exchange information and material with their environment. Large particles often get wrapped by membranes, a process which has been intensively…
In gas evolving electrolysis, bubbles grow at electrodes due to a diffusive influx from oversaturation generated locally in the electrolyte by the electrode reaction. When considering electrodes of micrometer-size resembling catalytic…
Systems of PDEs comprised of a combination of constraints and evolution equations are ubiquitous in physics. For both theoretical and practical reasons, such as numerical integration, it is desirable to have a systematic understanding of…
The problem of the diffusion evolution of a pore filled with molecular hydrogen in a spherical granule in a hydrogen medium is solved. The initial position of the pore is displaced relative to the center of the granule. A nonlinear system…
Understanding the mechanical instabilities of two-dimensional membranes has strong connection to the subjects of structure instabilities, morphology control and materials failures. In this work, we investigate the plastic mechanism…
We study the mathematical evolution of a liquid fuel droplet inside a vessel. In particular, we analyze the evolution of the droplet radius on a finite time interval. The model problem involves an hyperbolic system coupled with the pressure…
Cell proliferation, apoptosis, and myosin-dependent contraction can generate elastic stress and strain in living tissues, which may be dissipated by internal rearrangement through cell topological transition and cytoskeletal reorganization.…
We establish the most general form of the discrete elasticity of a 2D triangular lattice embedded in three dimensions, taking into account up to next-nearest neighbour interactions. Besides crystalline system, this is relevant to biological…
We systematize and extend the description of vesicle growth and shape change using linear nonequilibrium thermodynamics. By restricting the study to shape changes from spheres to axisymmetric ellipsoids, we are able to give a consistent…