A theory of passive ion flux through axon membranes
Passive ion flux through axon membranes
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Passive ion flux through axon membranes
The theory, variational formulation and finite element analysis of a class of nonlinear problems arising in optimization, thin membrane deflection and compressible flows are developed. Error estimates are summarized, and representative numerical results are presented. Particular theoretical questions pertaining to the existence and uniqueness of solutions are addressed, and their implications for such applications of finite element analysis as the study of compressible flows indicated.
The theory of liquid films and thin jets as one- and two-dimensional continuums is examined. The equations of motion have led to solutions for the characteristic speeds of wave propagation for the parameters characterizing the shape. The formal analogy with a compressible fluid indicates the possibility of shock wave generation in films and jets and the formal analogy to the theory of threads and membranes leads to the discovery of some new dynamic effects. The theory is illustrated by examples.
Membrane pores are implicated in several critical functions, including cell fusion and the transport of signaling molecules for intercellular communication. However, these structural features are often difficult to probe directly. Droplet interfacial bilayers offer a synthetic platform to study such membrane properties. We develop a theory that links size-selective transport across a metastable membrane with its transient structural properties. The central quantity of our theory is a dynamic permeability that depends on the mechanism of pore growth, which controls the transient distribution of pore sizes in the membrane. We present a mechanical perspective to derive pore growth dynamics and the resulting size distribution for growth via Ostwald ripening and discuss how these dynamics compare to other growth mechanisms such as coalescence and growth through surfactant desorption. We find scaling relations between the transported particle size, the pore growth rate, and the time for a given fraction of particles to cross the membrane, from which one may deduce the dominant mechanism of pore growth, as well as material properties and structural features of the membrane. Finally, we suggest experiments using droplet interfacial bilayers to validate our theoretical predictions.
The effects of a pulse shape on the transient response of a cylindrical shell are presented. Uniaxial, membrane, and bending theories for isotropic shells were used in this study. In addition to the results of the analytical study, the preliminary results of an experimental study into the generation and measurement of shear waves in a cylindrical shell are included.
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Modifications to condenser microphone theory yield new expressions for the membrane deflections at its center, which provide the basic theory for the fiber optic microphone. The theoretical analysis for the membrane amplitude and the phase response of the fiber optic microphone is given in detail in terms of its basic geometrical quantities. A relevant extension to the original concepts of the optical microphone includes the addition of a backplate with holes similar in design to present condenser microphone technology. This approach generates improved damping characteristics and extended frequency response that were not previously considered. The construction and testing of the improved optical fiber microphone provide experimental data that are in good agreement with the theoretical analysis.
Abstract Porous graphene and other atomically thin 2D materials are regarded as highly promising membrane materials for high‐performance gas separations due to their atomic thickness, large‐scale synthesizability, excellent mechanical strength, and chemical stability. When these atomically thin materials contain a high areal density of gas‐sieving nanoscale pores, they can exhibit both high gas permeances and high selectivities, which is beneficial for reducing the cost of gas‐separation processes. Here, recent modeling and experimental advances in nanoporous atomically thin membranes for gas separations is discussed. The major challenges involved, including controlling pore size distributions, scaling up the membrane area, and matching theory with experimental results, are also highlighted. Finally, important future directions are proposed for real gas‐separation applications of nanoporous atomically thin membranes.
Block copolymer self-assembly in conjunction with nonsolvent-induced phase separation (SNIPS) has been increasingly leveraged to fabricate integral-asymmetric membranes. The large number of formulation and processing parameters associated with SNIPS, however, has prevented the reliable construction of high performance membranes. In this study, we apply dynamical self-consistent field theory to model the SNIPS process and investigate the effect of various parameters on the membrane morphology: solvent selectivity, nonsolvent selectivity, initial film composition, and glass transition composition. We examine how solvent selectivity and concentration of polymers in the film impact the structure of micelles that connect to form the membrane matrix. In particular, we find that preserving the order in the surface layer and forming a connection between the supporting and surface layer are nontrivial and sensitive to each parameter studied. Furthermore, the effect of each parameter is discussed, and suggestions are made for successfully fabricating viable block copolymer membranes.
Here, we reported a strategy of using an eggshell membrane to produce hierarchically porous carbon as a low-cost substrate for synthesizing a nano-nickel oxide catalyst (C@NiO), which can effectively turn biowaste—urea—into energy through an electrochemical approach. Here, the interwoven carbon networks within NiO led to highly efficient urea oxidation due to the strong synergistic effect. The as-prepared electrode only needed 1.36 V versus reversible hydrogen electrode to realize a high efficiency of 10 mA cm –2 in 1.0 M KOH with 0.33 M urea and delivered an even higher current density of 25 mA cm –2 at 1.46 V, which is smaller than that of the porous carbon and commercial Pt/C catalyst. Benefiting from theoretical calculations, Ni(III) active species and the porous carbon further enabled the electrocatalyst to effectively inhibit the “CO 2 poisoning” of electrocatalysts, as well as ensuring its superior performance for urea oxidation.
Magnesium batteries offer a safer alternative for next-generation battery technology due to their insusceptibility to dendrite deposition. Selective membranes tailored for magnesium-ion conduction will unlock further technological advancement. Herein, we demonstrate fluorine-free magnesiated sulfonated poly(ether ether ketone) (Mg-SPEEK) selective membranes capable of facilitating magnesium-ion conduction while effectively rejecting soluble organic species. These membranes demonstrate a reversible Mg plating and stripping Coulombic efficiency (CE) of 85.4% and an ionic conductivity of 3.3 × 10 –4 S cm –1 at room temperature, surpassing those for a Mg-Nafion selective membrane. Theoretical density functional theory (DFT) calculations reveal that SPEEK possesses more localized charge centers along its backbone compared with Nafion, potentially facilitating enhanced ion conduction. Finally, full cells assembled with Mg-SPEEK coupled with the organic cathode pyrene-4,5,9,10-tetraone (PTO) and Mg metal demonstrated significantly improved capacity retention as compared to those assembled with conventional nonselective separators.
Here, we present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff–Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell’s mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith’s theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires C 1 -continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-α method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton–Raphson scheme. Finally, the interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.
The use of ion exchange membranes (IEMs) for electrochemical ion-ion separation leverages the selectivity of the IEMs toward like-charged species via valence difference and/or other ion membrane interactions. A mechanistic model that relates selectivity with membrane structural and chemical properties is lacking in the literature. Here, in this study, we extend the Manning’s counter-ion condensation model for describing ion partition and ion mobility inside IEMs to mixed salts scenarios. We evaluate the extended Donnan-Manning model against experimental data from literature and compare the performance the Donnan-Manning model to that of the ideal Donnan model and the Donnan-Affinity model. Our analysis shows that, despite its structural complexity, the Donnan-Manning model has less fitting parameters than the Donnan-Affinity model and generally outperforms the two other models in predicting counter-ion and co-ion partition. With the assumption of a higher mobility of condensed ions than that of uncondensed ions, the generalized Manning’s model can also predict counter-ion mobility selectivity for cation exchange membranes, but its performance for predicting mobility selectivity for anion exchange membranes is still unsatisfactory.
The formation of nanoscale bubbles is an unavoidable consequence during the transfer of two-dimensional materials onto target substrates, driven by van der Waals interactions at the interface. While often viewed as imperfections, these nanoscale bubbles have garnered considerable scientific interest due to the substantial in-plane strain gradients they induce, which in turn give rise to a variety of intriguing optoelectronic effects, particularly in semiconducting transition metal dichalcogenides. Determining and analyzing the strain distribution within nanobubbles at the nanoscale is crucial for advancing our understanding of these underlying strain-induced effects. Here, we present a high-resolution scanning tunneling microscopy-based tip-enhanced Raman spectroscopic investigation of localized nanoscale strain distribution within the nanobubbles formed between monolayer MoS 2 and Au interface. By employing cryogenic temperature (78 K), we successfully differentiate the nanoscale Raman signatures between nanobubble edge and pristine MoS 2 . We verify a maximum tensile strain of ∽1.15–1.34% at the nanobubble edge, which gradually diminishes toward the center, yielding a cross-sectional strain profile consistent with a doughnut-shaped distribution. Furthermore, we report to achieve ∽5 nm spatial resolution in probing such edge-localized strain within the nanobubble. In addition, comparative average strain analysis of such MoS 2 nanobubbles is conducted via geometric mechanistic analysis such as membrane and nonlinear plate theories, providing key insight into the geometric nature near the bubble edge. Our work provide fundamental information about strain-induced nanoscale chemical understanding of 2D materials on the nanometer scale, paving the way for practical applications of nanobubbles in strain-engineered optoelectronic devices.
Thin solar sail membranes of very large span are being envisioned for near-term space missions. One major design issue that is inherent to these very flexible structures is the formation of wrinkling patterns. Structural wrinkles may deteriorate a solar sail's performance and, in certain cases, structural integrity. In this paper, a geometrically nonlinear, updated Lagrangian shell formulation is employed using the ABAQUS finite element code to simulate the formation of wrinkled deformations in thin-film membranes. The restrictive assumptions of true membranes, i.e. Tension Field theory (TF), are not invoked. Two effective modeling strategies are introduced to facilitate convergent solutions of wrinkled equilibrium states. Several numerical studies are carried out, and the results are compared with recent experimental data. Good agreement is observed between the numerical simulations and experimental data.
Inflatable membrane reflectors are attractive for deployable, large aperture, lightweight optical and microwave systems in micro-gravity space environment. However, any fabrication flaw or temperature variation may results in significant aberration of the surface. Even for a perfectly fabricated inflatable membrane mirror with uniform thickness, theory shows it will form a Hencky curve surface but a desired parabolic or spherical surface. Precision control of the surfaceshape of extremely flexible membrane structures is a critical challenge for the success of this technology. Wirelessly controllable inflated reflectors made of electroactive polymers (EAP) are proposed in this paper. A finite element model was configured to predict the behavior of the inflatable EAP membranes under pre-strains, pressures and distributed electric charges on the surface. To explore the controllability of the inflatable EAP reflectors, an iteration algorism was developed to find the required electric actuation for correcting the aberration of the Hencky curve to the desired parabolic curve. The correction capability of the reflectors with available EAP materials was explored numerically and is presented in this paper.