On one case of quasi-correctness of the static boundary value problem for shells of rotation

Within the framework of the membrane theory of convex shells, a static boundary value problem is studied for one class of spherical domes.

Bit threads and the membrane theory of entanglement dynamics

Recently, an effective membrane theory was proposed that describes the “hydrodynamic” regime of the entanglement dynamics for general chaotic systems. Motivated by the new bit threads formulation of holographic entanglement entropy, given in terms of a convex optimization problem based on flow maximization, or equivalently tight packing of bit threads, we reformulate the membrane theory as a max flow problem by proving a max flow-min cut theorem. In the context of holography, we explain the relation between the max flow program dual to the membrane theory and the max flow program dual to the holographic surface extremization prescription by providing an explicit map from the membrane to the bulk, and derive the former from the latter in the “hydrodynamic” regime without reference to minimal surfaces or membranes.

Inevitable Variance of Electric Field of Plasma Membrane

An embryonic version of membrane theory can be date back to the Bernstein's work reported more than a hundred years ago. Such an originally old work has evolved conceptually and mathematically up until today, and it plays a central role in current membrane theory. Goldman-Hodgkin-Katz equation (GHK eq.) is one of the math-based monumental works, which constitutes the present membrane theory. Goldman theoretically derived GHK eq., but its physiological meaning was provided by the two renowned scientists, Hodgkin and Katz. These two employed an assumption that the electric field (EF) across the plasma membrane is constant to validate the GHK eq. physiologically. Proposal of Hodgkin-Huxley model (HH model) is another math-based monumental works developed from the membrane theory and now forms a fundamental part of the current membrane theory. GHK eq. and HH model are quite fundamental central concepts in the current physiology. Despite the broad acceptance of GHK eq. at present time, its prerequisite that the EF within the plasma membrane is constant is hardly believable. Especially when the action potential is generated, it sounds totally nonsense. Furthermore, the existence of constant EF within the plasma membrane is conceptually almost in conflict with the HH model. The authors will discuss those problematic issues the membrane theory inherits.

What Membrane Capacitance?

The most common and taught membrane theory assumes that the membrane behaves as a kind of electrical capacitance that is exposed to an electrical current generated by an ionic flow. If this statement is verifiable, it can be confirmed by the laws of physics, mathematics and in particular electricity. We will demonstrate that this hypothesis is not verified and that it is necessary to modify biophysics according to already established and experimentally verified principles of physics.

Explaining trans-phase potential differences with membrane theory, association-induction hypothesis and murburn concept

The characteristics of the experimentally measured trans-membrane potential (TMP) generated across an artificial membrane intervening two KCl solutions were found to be explicable using simple principles of electrochemistry, as given within the context of Association Induction Hypothesis (AIH). AIH suggests that the heterogeneous ion distribution which is caused by the adsorption of a mobile ion onto an immobile phase (bearing charge opposite to that of the mobile ion) is responsible for the TMP generation. Therefore, this work proposes AIH could be an important foundation for explaining the origin of TMP. Our experimental observation of nonzero TMP across an electrically charged non-biological/synthetic membrane is found to be intriguing, as such outcomes are classically associated to ion-pumping activities of membrane proteins in a living matter. Another experimental observation of nonzero potential across a neutral membrane is even more intriguing. Such a potential behavior is more in harmony with murburn concept, a new proposal for explaining redox metabolic and physiological phenomena.

Gol'denveizer Problem of Elastic Torus

The Gol'denveizer problem of a torus can be described as follows: a toroidal shell is loaded under axial forces and the outer and inner equators are loaded with opposite balanced forces. Gol'denveizer pointed out that the membrane theory of shells is unable to predict deformation in this problem, as it yields diverging stress near the crowns. Although the problem has been studied by Audoly and Pomeau (2002) with the membrane theory of shells, the problem is still far from resolved within the framework of bending theory of shells. In this paper, the bending theory of shells is applied to formulate the Gol'denveizer problem of a torus. To overcome the computational difficulties of the governing complex-form ordinary differential equation (ODE), the complex-form ODE is converted into a real-form ODE system. Several numerical studies are carried out and verified by finite-element analysis. Investigations reveal that the deformation and stress of an elastic torus are sensitive to the radius ratio, and the Gol'denveizer problem of a torus can only be fully understood based on the bending theory of shells.