Membrane Theory Research Articles

Comment on “Fluid energy theory of membrane”, published by Li et al. [Water Res. 260 (2024) 121900]

Comment on “Fluid energy theory of membrane”, published by Li et al. [Water Res. 260 (2024) 121900]

Entanglement membrane in exactly solvable lattice models

Entanglement membrane theory is an effective coarse-grained description of entanglement dynamics and operator growth in chaotic quantum many-body systems. The fundamental quantity characterizing the membrane is the entanglement line tension. However, determining the entanglement line tension for microscopic models is in general exponentially difficult. We compute the entanglement line tension in a recently introduced class of exactly solvable yet chaotic unitary circuits, so-called generalized dual-unitary circuits, obtaining a nontrivial form that gives rise to a hierarchy of velocity scales with vE<vB. For the lowest level of the hierarchy, L¯2 circuits, the entanglement line tension can be computed entirely, while for the higher levels the solvability is reduced to certain regions in spacetime. This partial solvability enables us to place bounds on the entanglement velocity. We find that L¯2 circuits saturate certain bounds on entanglement growth that are also saturated in holographic models. Furthermore, we relate the entanglement line tension to temporal entanglement and correlation functions. We also develop methods of constructing generalized dual-unitary gates, including constructions based on complex Hadamard matrices that exhibit additional solvability properties and constructions that display behavior unique to local dimension greater than or equal to three. Our results shed light on entanglement membrane theory in microscopic Floquet lattice models and enable us to perform nontrivial checks on the validity of its predictions by comparison to exact and numerical calculations. Moreover, they demonstrate that generalized dual-unitary circuits display a more generic form of information dynamics than dual-unitary circuits. Published by the American Physical Society 2024

Re-designing demolished Cultural Heritage. A study of a thin shell design for earthquake-destroyed churches in Finiq municipality

This scientific study involves the methods for the design of thin shells on top of cultural heritage buildings that have already collapsed in the municipality of Finiq. The studied object is an orthodox church in Finiq municipality, in Leshnica e Sipërme village. Its roof has already collapsed because of an earthquake and the degradation of the mate- rial. However, the dominant part of the structure, such as walls and columns, is still standing, even though need reinforcement. The maximum span of the roof is long enough to justify the use of a thin shell structure. This study tries to find an elegant solution to this problem, which combines structural beauty with the efficiency of the design and building process, defined as important aspects of a good structural design. The methods proposed for the reconstruction of the existing part of the church are the restoration methods used for monuments in Albania. The propositions take into consideration the state of degradation of each structural element. The primary goal for the reconstruction of the reinforcing elements is that they will not affect the primary function of the building and to restore and keep the cultural heritage values of the object. The pre-design of the roof is made using non-linear analyses. The shape of the new roof and its thickness are chosen to use the Hanging Model Analysis, the Sanders-Koiter equations, the Membrane Theory and a buckling analysis using the software Karamba. The designing of rigid joints, which connect the roof with the other part of the structure, is made so that the entire structure could work and behave as one, while it is loaded during its lifespan. The shell is designed as a pre-fabricated one using UHPC material and divided into panels with rigid joints between them. The analysis and validation of the design of the structure is made with the Load Capacity Analysis in the Ultimate Limit State of it using the software Karamba. The paper concludes by highlighting the importance of recovering the already degraded cultural heritage structures and the role that technology can play in ensuring the integration of the old part of the structure with the new one.

Morphological Influence on a Nonionic Bilayer Bending Rigidity and Compression Modulus.

The mechanical properties of multilamellar vesicles and their relevance to soft matter physics and material science are of significant interest. The bending rigidity, κ, and compression modulus, B, of three-dimensional (3D) finite nonspontaneous multilamellar vesicles, formed by a nonionic surfactant, are linked to nanoscale bilayer thickness, δ, estimated via small-angle X-ray scattering, and macroscopic elastic modulus measured through small-amplitude oscillatory shear experiments. κ and B significantly differ from the same system in the two-dimensional (2D) infinite nanostructured planar lamellar phase. Particularly, κ3D was found to be much smaller than κ2D, while an opposite behavior was seen for B. The 2D-to-3D morphology transition occurs under a transient mechanical field, resulting in rheopectic behavior. κ scales quadratically with δ, consistent with bilayer membrane theories, and linearly with vesicle radius in the densely packed state. These findings have implications for understanding and designing soft interfaces due to the influence of bending rigidity on transport properties.

Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics

The Hayden-Preskill protocol probes the capability of information recovery from local subsystems after unitary dynamics. As such it resolves the capability of quantum many-body systems to dynamically implement a quantum error-correcting code. The transition to coding behavior has been mostly discussed using effective approaches, such as entanglement membrane theory. Here, we present exact results on the use of Hayden-Preskill recovery as a dynamical probe of scrambling in local quantum many-body systems. We investigate certain classes of unitary circuit models, both structured Floquet (dual-unitary) and Haar-random circuits. We discuss different dynamical signatures corresponding to information transport or scrambling, respectively, that go beyond effective approaches. Surprisingly, certain chaotic circuits transport information with perfect fidelity. In integrable dual-unitary circuits, we relate the information transmission to the propagation and scattering of quasiparticles. Using numerical and analytical insights, we argue that the qualitative features of information recovery extend away from these solvable points. Our results suggest that information recovery protocols can serve to distinguish chaotic and integrable behavior, and that they are sensitive to characteristic dynamical features, such as long-lived quasiparticles or dual-unitarity.

A shell theory approach for the analysis of metal-FRP hybrid toroidal pressure vessels

This study focuses on the analysis of metal-FRP hybrid toroidal pressure vessels (TPV) using shell theory. The analytical approaches for the design of metal-FRP TPVs considering bending effects are currently not available. Invariably the designs are done based on the most simplified approach like linear membrane theory. In this work, a potential energy functional for the metal-FRP TPV considering the membrane and bending deformations is developed using Love's shell theory. The classical laminate theory is employed to determine the stresses/strains throughout the thickness of the FRP laminate. The Rayleigh-Ritz method is adopted to solve the proposed potential energy functional. A finite element analysis (FEA) is conducted using ABAQUS to validate the proposed analytical solution. In addition, a parametric analysis is carried out to understand the influence of various parameters viz. thickness of base metal, thickness of FRP, and ratio between radii of toroid and cross-section on bending deformations in the hybrid TPV. The results from the proposed solution are in good agreement with that from FEA. Therefore, the proposed solution can be used in the analysis and design of the metal-FRP TPV irrespective of any variations in the geometric parameters. It is found that the inclusion of bending deformations can improve the accuracy of solution and the bending deformations in the base metal decreases or become negligibly small with the increase in R/r ratio and thickness of FRP. The orientation of fibers can change the direction of failure in the base metal. The important design parameters that influence the yield pressure are thickness of base metal and FRP, orientation of fibers and R/r ratio.

Analysis of deformation and multi-angle tip contact in a combined mechanism of thin-walled membrane forces and inextensible layers in soft actuators

Soft actuators have extensive applications in operations, are generally made of elastomers, and generate large deformation. It makes accurately predicting their deformation behavior challenging. This study considers the combined effects of chamber sidewall expansion and inextensible layer strain mechanisms on the actuator's bending and tip contact force. We separately model the expansion of the chamber sidewall and the strain in the inextensible layer using the expanding membrane and strain beam theory. The theoretical model presented to predict the contact area of the sidewall expanding membrane under multiple bending conditions. The analytical models for three actuator states are established: 1) Free space; 2) Tip contact at multiple angles; and 3) Grasping state. The proposed theoretical model accurately predicts deformation, force characteristics, and the requisite pressure for object grasping, and its applicability extends to similar soft actuators. Comparative analyses with finite element methods (FEM) and experimental results validate the model's computational efficiency, reduced design variables, and accurate prediction of diverse deformations and tip contact forces. Notably, the model outperforms with shorter computation times. The large and small chamber spacing errors are approximately 10 % and 5 %, respectively.

Natural Bioactive Compounds as Anti-aging Agents: Current and Future Perspectives

Abstract: Aging is a natural biological process that occurs due to various factors like unhealthy diet, environmental factors, genetic factors, and lack of moisture. This process leads to the loss of skin elasticity, also known as sagging. It happens due to the gradual decline of collagen type VII (Col-7) and fibril, which slows down the connection between the dermis and epidermis layers, causing the skin to look aged externally. There are several theories of aging, such as the free radical theory, membrane theory, DNA or genetic theory, neuroendocrine theory, telomerase theory, mitochondrial decline theory, and Hayflick limit theory. According to WHO, by 2030, one in six individuals worldwide will be 60 years or older. There are synthetic compounds available in the market for anti-aging purposes, but they pose various side effects. Natural products play an essential role in managing aging, and anti-aging phytoconstituents are mostly found in plant parts like fruits, stems, roots, and other plant sources that have no side effects. This review focuses on various anti-aging agents derived from plants and other natural sources.

Indentation of circular hyperelastic membrane with hole by cylindrical indenter

We consider the problem of indentation of a thin circular elastic plate with a hole in the centre by a cylindrical indenter under large strains. We use the nonlinear theory of isotropic incompressible hyperelastic membranes and consider a quasi-static process of indentation. We use Coulomb’s law to describe the friction at a contact. The goals of this study are to determine and to compare the effects of friction, material parameters and pre-stretch of the membrane on the indentation process.

The Long Journey from Animal Electricity to the Discovery of Ion Channels and the Modelling of the Human Brain.

This retrospective begins with Galvani's experiments on frogs at the end of the 18th century and his discovery of 'animal electricity'. It goes on to illustrate the numerous contributions to the field of physical chemistry in the second half of the 19th century (Nernst's equilibrium potential, based on the work of Wilhelm Ostwald, Max Planck's ion electrodiffusion, Einstein's studies of Brownian motion) which led Bernstein to propose his membrane theory in the early 1900s as an explanation of Galvani's findings and cell excitability. These processes were fully elucidated by Hodgkin and Huxley in 1952 who detailed the ionic basis of resting and action potentials, but without addressing the question of where these ions passed. The emerging question of the existence of ion channels, widely debated over the next two decades, was finally accepted and, a decade later, many of them began to be cloned. This led to the possibility of modelling the activity of individual neurons in the brain and then that of simple circuits. Taking advantage of the remarkable advances in computer science in the new millennium, together with a much deeper understanding of brain architecture, more ambitious scientific goals were dreamed of to understand the brain and how it works. The retrospective concludes by reviewing the main efforts in this direction, namely the construction of a digital brain, an in silico copy of the brain that would run on supercomputers and behave just like a real brain.

Fluid energy theory of membrane

Membrane science is the key strategy to solve water shortage in the future, and its essence is energy and mass transfer. Due to the complexity and variety of the internal structure of membrane, the energy transfer theory of membrane is still a black box theory. Herein, a new fluid mechanics principle is introduced to establish the energy fluid theory of membrane, which is translated into the energy formula: such as the initial total pressure difference (ΔP), the flow rate of fluid exiting the membrane (v1 and v2), fluid density (ρ), and energy consumption by salt resistance (NSR): {ΔP2ΔPρ=ΔP2ΔPρ[1−v1ρ2ΔP]+NSR+[ΔPv1(v2v1)2−12ρv23]+12ρv23}. The theoretical framework is not only helpful for the data analysis of the energy transfer process of membranes, but also helps to allow for more in-depth and specific theoretical research. For instance, the relationship between NSR and the concentration difference (C) of salt can be expressed as NSR = aCb (a-product constant, b-exponential constant, R2>0.99). Hence, the basic theory can not only be widely applied to a variety of membranes with complex internal structure, but also have a profound impact on the application and research of membrane science.

Isometric deformations of discrete and smooth T-surfaces

Quad-surfaces are polyhedral surfaces with quadrilateral faces and the combinatorics of a square grid. Isometric deformation of the quad-surfaces can be thought of as transformations that keep all the involved quadrilaterals rigid. Among quad-surfaces, those capable of non-trivial isometric deformations are identified as flexible, marking flexibility as a core topic in discrete differential geometry. The study of quad-surfaces and their flexibility is not only theoretically intriguing but also finds practical applications in fields like membrane theory, origami, architecture and robotics.A generic quad-surface is rigid, however, certain subclasses exhibit a 1-parameter family of flexibility. One of such subclasses is the T-hedra which are originally introduced by Graf and Sauer in 1931.This article provides a synthetic and an analytic description of T-hedra and their smooth counterparts namely, the T-surfaces. In the next step the parametrization of their isometric deformation is obtained and their deformability range is discussed. The given parametrizations and isometric deformations are provided for general T-hedra and T-surfaces. However, specific subclasses are extensively examined and explored, particularly those that encompass notable and well-known structures, including the Miura fold, surfaces of revolution and molding surfaces.

Fracture analysis of hyperelastic membrane using bond-associated non-ordinary state-based peridynamics

In this paper, a non-ordinary state-based peridynamics model (NOSB PD) has been proposed to simulate the large deformation and failure analysis of hyperelastic membranes. To account for the curving horizon of the membrane, a non-local membrane theory has been developed by approximating it as a flat surface and applying the plane stress assumption locally. Thus, the membrane structure is simulated using a single layer of material points, which simplifies implementation, improves efficiency, and avoids volume locking. The Gent model has been employed to simulate the hyperelastic material constitutively, as it has an elegant mathematical framework and can achieve the entire range of stretches. Furthermore, Bond-associate NOSB PD is utilized to overcome zero-energy modes without affecting the material properties. A modification has been addressed to overcome the boundary effect by adding a complementary force density to the boundary nodes. The accuracy of large deformation and incompressibility of the developed models are verified by the corresponding finite element analyses. Finally, the proposed method is demonstrated by presenting some benchmark examples, and the results illustrate the accuracy and efficiency of the proposed method for the large deformation, fracture, and off-plane tearing analyses of hyperelastic membranes.

On the boundary conditions for a thin circular plate conjugated to a massive body

The problem of deformation under the action of uniform pressure of a circular plate coupled with a massive base is considered, while the condition for the coupling of the plate with the base is modeled using boundary conditions of the generalized elastic embedding type, i.e. the relationship between the bending moment and forces at the edge of the plate with displacements and rotation angles through the compliance matrix. The main goal of the work is to study the influence of the elasticity of the embedding on the elastic response of the plate. The solution to the problem was obtained in the formulation of the linear theory of plates, the theory of membranes in the approximation of homogeneity of longitudinal forces, and the Foppl — von Karman theory, also in the approximation of the assumption of homogeneity of longitudinal forces. The values of the coefficients of the compliance matrix were obtained using the finite element method for the auxiliary problem and compared with the values of the coefficients obtained for related problems by analytical methods. Numerical results were obtained for an aluminum wafer on a silicon base. The obtained solution was compared with the solution obtained for the rigid embedment condition for all three models used. It is shown that in the case of large deflections (several plate thicknesses), taking into account the compliance of the embedment becomes essential.

Multi-factors effects analysis of nonlinear vibration of FG-GNPRC membrane using machine learning

Functionally graded graphene nanoplatelet reinforced composite (FG-GNPRC) have exhibited significant potential for the development of high-performance and multifunctional structures. In this paper, we present a machine learning (ML) assisted uncertainty analysis of nonlinear vibration of FG-GNPRC membranes under the influence of multi-factor coupling. Effective medium theory (EMT), Mori-Tanaka (MT) model and rule of mixture are utilized to evaluate the effective material properties of the composite membrane. Governing equations are derived via an energy method with the frameworks of the hyperelastic membrane theory, Neo-Hookean constitutive model and the couple dielectric theory. Randomly generated inputs after data pre-processing are fed into governing equations, which are solved by numerical methods for outputs. Three ML models, including artificial neural network (ANN), support vector regression (SVR) and AutoGluon-Tabular (AGT), are adopted to capture the complex relationship between the systematic inputs (i.e., structural dimensions, attributes of GNPs and pores, external electric field, etc.), frequency ratio and dimensionless amplitude of FG-GNPRC membranes. The results demonstrate that all three ML models demonstrate exceptional computational efficiency, and AGT presents higher prediction accuracy compared to the other two models. Based on the Shapley additive explanations (SHAP) approach, the effects of uncertainties of system parameters and multi-factor coupling on the nonlinear vibration of the FG-GNPRC membrane are analyzed. It is found that the uncertainty of structural parameters has the greatest impact on the nonlinear vibration of FG-GNPRC membranes, particularly when the membrane is subjected to a voltage of 10 V and smaller stretching ratio.

Interference effect and Raman depolarization behavior in MoO2 bubbles

Here, MoO2 bubbles are firstly found in MoO2 nanosheets (NSs) synthesized by chemical vapor deposition and exposed to air for 2–3 years. Interestingly, the Newton’s rings are clearly observed in Raman map of MoO2 bubbles. Meanwhile, it’s found that the height of bright rings close to the 1/2, 2/2, 3/2 of the laser wavelength, confirming that the Newton’s rings in Raman map are caused by the laser interference on the surface of bubbles. At the same time, based on simple membrane theory, the adhesion energy 0.15 and 1.08 J/m2 between MoO2 NSs and different SiO2/Si substrates are extracted. Moreover, Raman depolarization effect is observed on the surface of MoO2 bubbles. As the aspect ratio of bubbles increases from 0.16 to 0.21, the relative-depolarization ratios of 205 cm−1 and 750 cm−1 phonon modes are gradually increased from 18% to 46% and 10–36%, respectively. The Raman depolarization behavior should be ascribed to the surface strain of MoO2 bubbles leading to the asymmetric changes of photoelastic tensor in all directions of the crystal. This finding maybe provides a reference for regulating the polarization characteristics of MoO2 by adjusting its surface strain and ultimately achieving application in the field of photonics.

Application of perturbation-variation method in large deformation bimodular cylindrical shells: A comparative study of bending theory and membrane theory

A bimodular material is a kind of material that presents two elastic moduli in tension and compression. In the existing researches, the bimodular effect of materials is rarely considered due to its complexity in analysis. In this study, the large deformation problem of bimodular cylindrical shells is analytically and numerically investigated, in which the typical issue in cylindrical shells, using bending theory or membrane theory, is comparatively studied on the basis of large deformation. First, the large deformation governing equations on bimodular materials model are established under bending theory and membrane theory. A new analytical method, perturbation-variation method, is then used to obtain the theoretical solutions under bending theory and membrane theory. The numerical simulation also validates the theoretical solution obtained. The results show that the shape of cylindrical shells and the bimodular effect of materials have important influences on the relationship of load vs. central deflection and subsequent occurred jumping phenomenon. The rational use of both theories depends on many factors. Specifically, when the circumferential length of cylindrical shells is far greater than the longitudinal length, it is more reliable to adopt the membrane theory instead of the bending theory to analyze large deformation problem of bimodular thin cylindrical shells.

Antivesiculation and Complete Unbinding of Tail-Tethered Lipids.

We report the effect of tail-tethering on vesiculation and complete unbinding of bilayered membranes. Amphiphilic molecules of a bolalipid, resembling the tail-tethered molecular structure of archaeal lipids, with two identical zwitterionic phosphatidylcholine headgroups self-assemble into a large flat lamellar membrane, in contrast to the multilamellar vesicles (MLVs) observed in its counterpart, monopolar nontethered zwitterionic lipids. The antivesiculation is confirmed by small-angle X-ray scattering (SAXS) and cryogenic transmission electron microscopy (cyro-TEM). With the net charge of zero and higher bending rigidity of the membrane (confirmed by neutron spin echo (NSE) spectroscopy), the current membrane theory would predict that membranes should stack with each other (aka "bind") due to dominant van der Waals attraction, while the outcome of the nonstacking ("unbinding") membrane suggests that the theory needs to include entropic contribution for the nonvesicular structures. This report pioneers an understanding of how the tail-tethering of amphiphiles affects the structure, enabling better control over the final nanoscale morphology.

Inferring biophysical properties of membranes during endocytosis using machine learning.

Endocytosis is a fundamental cellular process in eukaryotic cells that facilitates the transport of molecules into the cell. With the help of fluorescence microscopy and electron tomography, researchers have accumulated extensive geometric data of membrane shapes during endocytosis. These data contain rich information about the mechanical properties of membranes, which are hard to access via experiments due to the small dimensions of the endocytic patch. In this study, we propose an approach that combines machine learning with the Helfrich theory of membranes to infer the mechanical properties of membranes during endocytosis from a dataset of membrane shapes extracted from electron tomography. Our results demonstrate that machine learning can output solutions that both match the experimental profile and satisfy the membrane shape equations derived from Helfrich theory. The learning results show that during the early stage of endocytosis, the inferred membrane tension is negative, indicating the presence of strong compressive forces at the boundary of the endocytic invagination. Our method presents a generic framework for extracting membrane information from super-resolution imaging.

Surface–dislocation interaction by various models of surface elasticity

The effect of applying different surface elasticity models related to the Gurtin–Murdoch and Steigmann–Ogden theories to the problem on an interaction of a dislocation row with a flat surface of a semi-infinite three-dimensional body is analyzed in the paper. The boundary conditions in the case of an arbitrary shape of a cylindrical surface under the plane strain are derived within the framework of the Steigmann–Ogden model involving all simplified versions of the Gurtin–Murdoch model and the Gurtin–Murdoch model itself. The boundary condition used in the paper for the flat surface is a particular case of the general one. The analytical solution of the corresponding boundary value problem is obtained in the paper in a closed form for the elastic field. Based on this solution, some numerical examples of the stress distribution at the surface and the image force acting on each dislocation are presented. It is shown that incorporating the bending resistance of the surface in the Steigmann–Ogden model leads to the decrease of some stresses and increase the other ones at the surface and to the decrease of the image force, as compared with those obtained by the Gurtin–Murdoch membrane theory of the surface.