We formulate a theory of the effects of long-range interactions on the surface tension and spontaneous curvature of proteinaceous shells based on the general Deryaguin-Landau-Verwey-Overbeek mesoscale approach to colloid stability. We derive the full renormalization formulas for the elastic properties of the shell and consider in detail the renormalization of the spontaneous curvature as a function of the corresponding Hamaker coefficient, inner and outer capsid charges, and bathing solution properties. The renormalized spontaneous curvature is found to be a nonmonotonic function of several parameters describing the system.
We have derived the free energy landscape for the translocation of a single vesicle through a narrow pore by accounting for bending and stretching of the vesicle, and the deformation of the vesicle by the pore. Emergence of a free energy barrier for translocation is a general result, and the magnitude of the barrier is calculated in terms of the various material parameters. The extent of the reduction in the barrier by the presence of an external constant force is calculated. Using the Fokker–Planck formalism, we have calculated the average translocation time corresponding to the various free energy landscapes representing different parameter sets. The dependencies of the average translocation time on the strength of the external force, vesicle size, bending and stretching moduli of the vesicle, and radius and length of the pore are derived, and the computed results are discussed.
Chatter is the most important limitation in high speed rolling of thin strips in modern industrial cold rolling mills. To study chatter in rolling, it is necessary to set up models for the rolling process as well as the mill stand. Existing models of the rolling process are analytic and are based on many simplifying assumptions. In current work Arbitrary Lagrangian Eulerian (ALE) finite element method is utilized for the first time to model the chatter vibrations in rolling, which relaxes many of these assumptions. The model has the benefit of mass translation to computational region by using ALE technique, which tremendously reduces huge computational requirements of the common Lagrangian models. The presented model is updated for simulating the chatter mechanism by means of some online velocity sensors and signal filtering method in applying the ALE boundary conditions. Results of the finite element model were compared with the experimental measurements obtained from a full scale industrial mill. Two main chattering characteristics, i.e., the critical rolling speed and the chatter frequency, obtained from the simulation program were found to be in good agreement with that of the experimental measurements.
We present a theory of adsorption of flexible polyelectrolytes on the interior and exterior surfaces of a charged vesicle in an electrolyte solution. The criteria for adsorption and the density profiles of the adsorbed polymer chain are derived in terms of various characteristics of the polymer, vesicle, and medium, such as the charge density and length of the polymer, charge density and size of the vesicle, electrolyte concentration and dielectric constant of the medium. For adsorption inside the vesicle, the competition between the loss of conformational entropy and gain in adsorption energy results in two kinds of encapsulated states, depending on the strength of the polymer-vesicle interaction. By considering also the adsorption from outside the vesicle, we derive the entropic and energy contributions to the free energy change to transfer an adsorbed chain in the interior to an adsorbed chain on the exterior. In this paper, we have used the Wentzel-Kramers-Brillouin (WKB) method to solve the equation for the probability distribution function of the chain. The present WKB results are compared with the previous results based on variational methods. The WKB and variational results are in good agreement for both the interior and exterior states of adsorption, except in the zero-salt limit for adsorption in the exterior region. The adsorption criteria and density profiles for both the interior and exterior states are presented in terms of various experimentally controllable variables. Calculation of the dependencies of free energy change to transfer an adsorbed chain from the interior to the exterior surface on salt concentration and vesicle radius shows that the free energy penalty to expel a chain from a vesicle is only of the order of thermal energy.
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