Dynamical evolution of heterogeneous nucleation on surfaces with ideal cavities

A theoretical investigation is conducted to explore the evolution behavior of heterogeneous nucleation on a solid surface with ideal conical cavities. According to the free energy characteristics of transition or a liquid–vapor phase change in an ideal conical cavity, the heterogeneous nucleation process can be divided into or described as three different types, nucleation within a cavity, nucleation outside a cavity and twice-nucleation. The nucleation within or outside a cavity only has one free energy barrier, and its nucleation rate can be derived from the classical theory. The twice-nucleation is concluded to occur in some special cavities, and its kinetic characteristic is different from the classical theory. The twice-nucleation rate is mainly determined by two free energy barriers as the free energy of a cluster at metastable state is positive. As the free energy of a cluster at metastable state is negative, the nucleation rate of twice-nucleation is determined not only by two energy barriers, but also dependent of the metastable state.     

A fluctuating elastic plate and a cell model for lipid membranes

The thermal fluctuations of lipid bi-layer membranes are key to their interaction with cellular components as well as the measurement of their mechanical properties. Typically, membrane fluctuations are analyzed by decomposing into normal modes or by molecular simulations. Here we propose two new approaches to calculate the partition function of a membrane. In the first approach we view the membrane as a fluctuating von Karman plate and discretize it into triangular elements. We express its energy as a function of nodal displacements, and then compute the partition function and co-variance matrix using Gaussian integrals. We recover well-known results for the dependence of the projected area of the membrane on the applied tension and recent simulation results on the dependence of membrane free energy on geometry, spontaneous curvature and tension. As new applications we compute the fluctuations of the membrane of a malaria infected cell and analyze the effects of boundary conditions on fluctuations. Our second approach is based on the cell model of Lennard-Jones and Devonshire. This model, which was developed for liquids, assumes that each molecule fluctuates within a cell on which a potential is imposed by all the surrounding molecules. We adapt the cell model to a lipid membrane by recognizing that it is a 2D liquid with the ability to deform out of plane whose energetic penalty must be factored into the partition function of a cell. We show, once again, that some results on membrane fluctuations can be recovered using this new cell model. However, unlike some well established results, our cell model gives an entropy that scales with the number of molecules in a membrane. Our model makes predictions about the heat capacity of the membrane that can be tested in experiments.     

Modeling biomembranes and red blood cells by coarse-grained particle methods

In this work, the previously developed coarse-grained (CG) particle models for biomembranes and red blood cells (RBCs) are reviewed, and the advantages of the CG particle methods over the continuum and atomistic simulations for modeling biological phenomena are discussed. CG particle models can largely increase the length scale and time scale of atomistic simulations by eliminating the fast degrees of freedom while preserving the mesoscopic structures and properties of the simulated system. Moreover, CG particle models can be used to capture the microstructural alternations in diseased RBCs and simulate the topological changes of biomembranes and RBCs, which are the major challenges to the typical continuum representations of membranes and RBCs. The power and versatility of CG particle methods are demonstrated through simulating the dynamical processes involving significant topological changes, e.g., lipid self-assembly vesicle fusion and membrane budding.     

Membrane fusion based on the geometry of the stalk model

It is a commonly accepted assumption that membrane fusion involves an hourglass-shaped local contact between two monolayers of opposing membranes, an intermediate structure called a stalk. The shape of the stalk is considered as an axisymmetrical figure of revolution in 3D space, with a planar geometry in the initial configuration. The total energy of the stalk is evaluated from the assumption that the stalk has a constant curvature. Its negative value due to the presence of spontaneous curvature promotes hemifusion. An extension of the original model developed in Markin and Albanesi [23] is proposed, in which any geometrical feature of the stalks can be expressed in explicit form, by considering the stalks as nodoid surfaces. The local stresses and induced internal moments due the membrane bending are evaluated based on the adopted parameterization.     

Mechanics of water pore formation in lipid membrane under electric field

Transmembrane water pores are crucial for sub-stance transport through cell membranes via membrane fusion, such as in neural communication. However, the molecular mechanism of water pore formation is not clear. In this study, we apply all-atom molecular dynamics and bias-exchange metadynamics simulations to study the pro-cess of water pore formation under an electric field. We show that water molecules can enter a membrane under an electric field and form a water pore of a few nanometers in diame-ter. These water molecules disturb the interactions between lipid head groups and the ordered arrangement of lipids. Fol-lowing the movement of water molecules, the lipid head groups are rotated and driven into the hydrophobic region of the membrane. The reorientated lipid head groups inside the membrane form a hydrophilic surface of the water pore. This study reveals the atomic details of how an electric field influences the movement of water molecules and lipid head groups, resulting in water pore formation.     

A model for lipid membranes with tilt and distension based on three-dimensional liquid crystal theory

The relationship between the two-dimensional theory of tilted lipid membranes and three-dimensional liquid crystal theory is discussed in detail. The latter framework furnishes an appropriate foundation for membrane theory and facilitates a straightforward reduction to a well-posed two-dimensional model. This emerges as a special case of the Cosserat theory of elastic shells and incorporates a model of generalized capillarity in which the membrane energy responds to surface curvature and also to surface dilation and its gradient.     

Clustering instability in adhesive contact between elastic solids via diffusive molecular bonds

Motivated by experimental observations that cell-cell and cell-matrix adhesion often involves formation of discrete patches of dense molecular bonds, we consider the plane strain problem of two elastic half-spaces, each covered with a layer of lipid membrane, joined together by mobile molecular bonds that diffuse along the interface under the combined action of a thin layer of glycocalyx repellers and an externally applied tensile stress. We show that, for a range of bond density values with or without the applied stress, the state of a uniform distribution of bonds is intrinsically unstable with respect to perturbations in bond density distribution. This instability is found to be primarily driven by elastic deformation energies in the bulk and the membrane. The change in free energy associated with a cosine perturbation in bond density distribution indicates that there exists a critical wavelength beyond which the perturbation becomes unstable and a fastest growing wavelength that tends to dominate as the instability grows. These length scales have typical values in the order of a micrometer, in agreement with the general characteristic size of bond clusters observed in cell adhesion.     

Solution for free vibration problem of membrane with unequal tension in two directions

In this paper, we obtain the analytic solution of free vibration frequency and mode shapes of rectangle, circle and elliptic membranes. The approximate solution of membrane with arbitrary boundary "is also obtained. All of these membranes are acted on by unequal tension in two directions.For the rectangle membrane, in this paper we transform its vibration equation into one of usual membranes by trnasforming the coordinate, thus it is easy to get the solution. For the circle membrane, first we transform the coordinate in the same way we deal with the rectangle membrane. Next we transform the vibration equation into the Mathieu equation, then we get a formula of frequency of that membrane with some Mathieu function’s property. In the solution the elliptic membrane is similar to that of the circle membrane.Finally, some examples are given.     

Structure and rheology of fiber-laden membranes via integration of nematodynamics and membranodynamics

This paper presents a study of the structure and dynamics of rigid fiber-laden deformable curved fluid membranes based on an viscoelastic model that integrates the statics of anisotropic membranes, the planar nematodynamics of fibers and the dynamics of isotropic membranes. Fiber-laden membranes arise frequently in biological systems, such as the plant cell wall and in protein–lipid bilayers. Based on the membrane's force and torque balance equations and the fiber's balance of molecular fields, a viscoelastic anisotropic model that provides the governing equations for the membrane's velocity and curvature and the fiber structure (fiber orientation and order) is found. A Helmholtz free energy that incorporates the tension/bending/and torsion membrane elasticity, the Landau–de Gennes fiber ordering, and fiber order-membrane curvature interactions is used to derive elastic moments, torques, and stresses. The corresponding viscous stresses and moments include the Boussinesq–Scriven contributions as well as bending, torsion, and rotational dissipation. A spectral decomposition leads to the main viscoelastic material functions for anisotropic fluid membranes. Applications of the rheological model to cylindrical growth and cylindrical axial stretching show that competing curvo-phobic, curvo-philic interactions under extensional flow predict transitions between axial and azimuthal fiber arrangements, of interest to cellulose fiber orientation in plant morphogenesis.     

Interactions of human islet amyloid polypeptide with lipid structure of different curvatures

Curvature is one of the most important features of lipid membranes in living cells, which significantly influences the structure of lipid membranes and their interaction with proteins. Taken the human islet amyloid polypeptide (hIAPP), an important protein related to the pathogenesis of type II diabetes, as an example, we performed molecular dynamics (MD) simulations to study the interaction between the protein and the lipid structures with varied curvatures. We found that the lipids in the high curvature membrane pack loosely with high mobility. The hIAPP initially forms H-bonds with the membrane surface that anchored the protein, and then inserts into the membrane through the hydrophobic interactions between the residues and the hydrophobic tails of the lipids. hIAPP can insert into the membrane more deeply with a larger curvature and with a stronger binding strength. Our result provided important insights into the mechanism of the membrane curvature-dependent property of proteins with molecular details.     

Computational analysis of liquid crystalline elastomer membranes: Changing Gaussian curvature without stretch energy

Liquid crystalline elastomers (LCEs) can undergo extremely large reversible shape changes when exposed to external stimuli, such as mechanical deformations, heating or illumination. The deformation of LCEs result from a combination of directional reorientation of the nematic director and entropic elasticity. In this paper, we study the energetics of initially flat, thin LCE membranes by stress driven reorientation of the nematic director. The energy functional used in the variational formulation includes contributions depending on the deformation gradient and the second gradient of the deformation. The deformation gradient models the in-plane stretching of the membrane. The second gradient regularises the non-convex membrane energy functional so that infinitely fine in-plane microstructures and infinitely fine out-of-plane membrane wrinkling are penalised. For a specific example, our computational results show that a non-developable surface can be generated from an initially flat sheet at cost of only energy terms resulting from the second gradients. That is, Gaussian curvature can be generated in LCE membranes without the cost of stretch energy in contrast to conventional materials.     

A theoretical consideration of the ballistic response of continuous graphene membranes

The remarkable properties of graphene, including unusually high mechanical strength and stiffness, have been well-documented. In this paper, we combine an analytical solution for ballistic impact into a thin isotropic membrane, with ab initio density functional theory calculations for graphene under uniaxial tension, to predict the penetration resistance of multi-layer graphene membranes. The calculations show that continuous graphene membranes could enable ballistic barriers of extraordinary performance, enabling resistance to penetration at masses up to 100× lighter than existing state-of-the-art barrier materials. The very high elastic wave speed and strain energy to failure are the major drivers of this increase in performance. However, the in-plane mechanical isotropy of graphene, as compared to conventional orthotropic woven textiles, also contributes significantly to the efficiency of graphene as a barrier material. This result suggests that, for barrier applications, isotropic membranes composed of covalently bonded two-dimensional molecular networks could provide distinct advantages over fiber-based textiles derived from linear polymers.     

A rate-dependent two-dimensional free energy model for ferroelectric single crystals

The one-dimensional free energy model for ferroelectric materials developed by Smith et al. [29–31] is generalized to two dimensions. The two-dimensional free energy potential proposed in this paper consists of four energy wells that correspond to four variants of the material. The wells are separated by four saddle points, representing the barriers for 90°-switching processes, and a local maximum, across which 180°-switching processes take place. The free energy potential is combined with evolution equations for the variant fractions based on the theory of thermally activated processes. The model is compared to recent measurements on BaTiO₃ single crystals by Burcsu et al. [8], and predicitions are made concerning the response to the application of in-plane multi-axial electric fields at various frequencies and loading directions. The kinetics of the 90°- and 180°-switching processes are discussed in detail.     

薄膜拉伸褶皱失稳力学进展

薄膜拉伸起皱现象在自然界和现代工业中普遍存在,在过去二十年里,引发了学者们极大的研究兴趣.这种起皱失稳行为源自薄膜能与弯曲能之间的非线性竞争.我们回顾从本世纪初至今薄膜拉伸褶皱失稳力学研究进展,将其分为两个阶段:前十年的研究主要局限于薄膜小应变(～1%)起皱现象,而后十年的兴趣主要集中在有限应变起皱-再稳定(孤立中心分岔)行为,在过度拉伸(～30%)时褶皱最终消失.定量理解、预测和追踪这种强非线性力学行为的需求推进了有限应变板壳理论和数值计算方法的发展,不仅促进了对薄膜起皱-消皱机理的深入理解,也为无褶皱膜结构设计和薄膜表面形貌调控提供了新的思路.     

Passive flow control by membrane wings for aerodynamic benefit

The coupling of passive structural response of flexible membranes with the flow over them can significantly alter the aerodynamic characteristic of simple flat-plate wings. The use of flexible wings is common throughout biological flying systems inspiring many engineers to incorporate them into small engineering flying systems. In many of these systems, the motion of the membrane serves to passively alter the flow over the wing potentially resulting in an aerodynamic benefit. In this study, the aerodynamic loads and the flow field for a rigid flat-plate wing are compared to free trailing-edge membrane wings with two different pre-tensions at a chord-based Reynolds number of approximately 50,000. The membrane was silicon rubber with a scalloped free trailing edge. The analysis presented includes load measurements from a sting balance along with velocity fields and membrane deflections from synchronized, time-resolved particle image velocimetry and digital image correlation. The load measurements demonstrate increased aerodynamic efficiency and lift, while the synchronized flow and membrane measurements show how the membrane motion serves to force the flow. This passive flow control introduced by the membranes motion alters the flows development over the wing and into the wake region demonstrating how, at least for lower angles of attack, the membranes motion drives the flow as opposed to the flow driving the membrane motion.     

The essence of neuronal activity from the consistency of two different neuron models

Based on the H–H equation, this study has proposed the calculation and analysis of energy expenditure for a single neuron which is activated at sup-threshold and subthreshold, as well as the criterion of the energy expenditure of neurons activated sup-threshold and subthreshold, which was the maximum power of a sodium ion pump. Results of the study showed that not only the electrophysiological activities of neurons were strictly restricted by the energy levels in the brain, but also the activities of neurons also had dual nature, meaning that subthreshold neurons were mainly with energy expenditure, while sup-threshold neurons were with both energy absorption and energy expenditure. These new findings were compared with the novel neuro-biophysical models that we have published last year, uncovering that the two models were essentially equivalent.     

Simultaneous solution of the Navier-Stokes and elastic membrane equations by a finite element method

Fluid flow through a significantly compressed elastic tube occurs in a variety of physiological situations. Laboratory experiments investigating such flows through finite lengths of tube mounted between rigid supports have demonstrated that the system is one of great dynamical complexity, displaying a rich variety of self-excited oscillations. The physical mechanisms responsible for the onset of such oscillations are not yet fully understood, but simplified models indicate that energy loss by flow separation, variation in longitudinal wall tension and propagation of fluid elastic pressure waves may all be important. Direct numerical solution of the highly non-linear equations governing even the most simplified two-dimensional models aimed at capturing these basic features requires that both the flow field and the domain shape be determined as part of the solution, since neither is known a priori. To accomplish this, previous algorithms have decoupled the solid and fluid mechanics, solving for each separately and converging iteratively on a solution which satisfies both. This paper describes a finite element technique which solves the incompressible Navier-Stokes equatikons simultaneously with the elastic membrane equations on the flexible boundary. The elastic boundary position is parametized in terms of distances along spines in a manner similar to that which has been used successfully in studies of viscous free surface flows, but here the membrane curvature equation rather than the kinematic boundary condition of vanishing normal velocity is used to determine these diatances and the membrane tension varies with the shear stresses exerted on it by the fluid motions. Bothy the grid and the spine positions adjust in response to membrane deformation, and the coupled fluid and elastic equations are solved by a Newton-Raphson scheme which displays quadratic convergence down to low membrane tensions and extreme states of collapse. Solutions to the steady problem are discussed, along with an indication of how the time-dependent problem might be approached.     

短纤维增强EPDM包覆薄膜超弹性本构模型

短纤维增强三元乙丙橡胶(EPDM)包覆薄膜用于一种新型缠绕包覆工艺,主要解决复杂构型自由装填药柱外表面可靠性包覆问题.为了描述其在固体火箭发动机工作过程中产生的大变形、非线性和各向异性等力学行为,根据纤维增强复合材料连续介质力学理论,提出了各向异性超弹性本构模型.该模型中单位体积的应变能函数被解耦成两部分:表征各向同性的橡胶基体应变能和表征各向异性的纤维拉伸应变能,通过引入纤维方向对纤维应变能进行修正,给出了通过单轴拉伸、偏轴拉伸实验数据获取模型参数的具体方法.研究结果表明,该模型能够很好地预测材料在纤维方向0°~45°时的各向异性力学特性,并将预测结果与实验数据对比,误差在5%以下.所建立的各向异性超弹性本构模型准确性高、易于实现数值开发,在一定程度上能够为固体火箭发动机的装药结构完整性分析提供理论依据.     

On the thermodynamics of fractional damping elements

Constitutive models of viscoelasticity in combination with fractional differential operators are successfully used by many authors to describe the mechanical properties of polymers. The topic of the present paper is the investigation of rheological models incorporating fractional damping elements from the point of view of thermodynamics. We take the Clausius Duhem inequality as admissibility criterion and investigate uniaxial and three-dimensional deformation processes at constant temperature. We specify sufficient conditions and show that rheological models, which consist of springs in combination with fractional dashpots, are compatible with the dissipation principle. As a new aspect of the subject, we present a systematic method for deriving the free energy functionals. With the help of two examples we demonstrate that the free energy of fractional systems can be derived as a generalisation of related discrete systems. To illustrate this method, we study in detail an isolated fractional dashpot (also known as a power-law model) and a fractional standard solid (Zener model). Finally, we propose a three-dimensional formulation of the fractional Zener model and specify the corresponding free energy functional. Received: July 3, 1996     

Free energies for singleton minimal states

It is assumed that any free energy function exhibits strict periodic behavior for histories that have been periodic for all past times. This is not the case for the work function, which, however, has the usual defining properties of a free energy. Forms given in fairly recent years for the minimum and related free energies of linear materials with memory have this property. Materials for which the minimal states are all singletons are those for which at least some of the singularities of the Fourier transform of the relaxation function are not isolated. For such materials, the maximum free energy is the work function, and free energies intermediate between the minimum free energy and the work function should be given by a linear relation involving these two quantities. All such functionals, except the minimum free energy, therefore do not have strict periodic behavior for periodic histories, which contradicts our assumption. A way out of the difficulty is explored which involves approximating the relaxation function by a form for which the minimal states are no longer singletons. A representation can then be given of an arbitrary free energy as a linear combination of the minimum, maximum and intermediate free energies derived in earlier work. This representation obeys our periodicity assumption. Numerical data are presented, supporting the consistency of this approach.