Microscopic membrane elasticity and interactions among membrane inclusions: interplay between the shape, dilation, tilt and tilt-difference modes

A phenomenological Landau elasticity for the shape, dilation, and lipid-tilt of bilayer membranes is developed. The shape mode couples with the sum of the monolayers' tilt, while the dilation mode couples with the difference of the monolayers' tilts. Interactions among membrane inclusions within regular arrays are discussed. Inclusions modifying the membrane thickness and/or inducing a tilt-difference due to their convex or concave shape yield a dilation-induced attraction and a tilt-difference-induced repulsion. The resulting interaction can stabilize 2D crystal phases, with the possible coexistence of different lattice spacings when the dilation-tilt-difference coupling is large. Inclusions favoring crystals are those with either a long-convex or a short-concave hydrophobic core. Inclusions inducing a local membrane curvature due to their conical shape repel one another. At short inclusions separations, a tilt comparable with the inclusion's cone angle develops: it relaxes the membrane curvature and reduces the repulsion. At large separations the tilt vanishes, whatever the value of the shape-tilt coupling. Received 23 October 1998 and Received in final form 12 January 1999     

The effects of cis–trans configuration of cyclohexane multi-carboxylic acids on colloidal forces in dispersions: steric, hydrophobic and bridging

The effects of cis- and trans-1,2-, trans-1,4-cyclohexanedicarboxylic acid, 95% cis-1,3,5-cyclohexane tricarboxylic acid and cis-1,2,3,4,5,6-cyclohexanehexacarboxylic acid on the yield stress–pH behaviour of concentrated ZrO₂ dispersions are reported. Adsorbed cis-1,2,3,4,5,6-cyclohexanehexacarboxylic acid imparts predominantly steric interactions. It forms a steric barrier keeping the interacting particles apart. Adsorbed cis- and trans-1,2 increase the maximum yield stress and this was attributed to a hydrophobic force resulting from the part of the cyclohexane ring sticking out into the solution which is devoid of charged or hydrophilic group. Adsorbed trans-1,4 increases the maximum yield stress by at least threefold and its configuration favours strong bridging interaction with an adjacent particle. Predominantly, cis-1,3,5 also increases the maximum yield stress but only by 60% at the same additive concentration. This was attributed to a smaller degree of bridging.     

Apparent hydrodynamic thickness of densely grafted polymer layers in a theta solvent

We study the drainage of a near-theta solvent through densely grafted polymer layers and compare to recent notions that these layers display little permeability to solvent flow at surface separations less than a “hydrodynamic thickness.” The solvent is trans-decalin (a near-theta solvent at the experimental temperature of 24°C). The polymer is polystyrene (PS) end-attached to two opposed mica surfaces via the selective adsorption of the polyvinylpyridine (PVP) block of a PS-PVP diblock copolymer. The experimental probe was a surface forces apparatus modified to apply small-amplitude oscillatory displacements in the normal direction. Out-of-phase responses reflected viscous flow of solvent alone—the PS chains did not appear to contribute to dissipation over the oscillation frequencies studied. The value of the hydrodynamic thickness (R_H) was less than the coil thickness (L_o) measured independently from the onset of surface–surface interactions in the force-distance profile, implying significant penetration of the velocity field into the polymer layer. As the surface–surface separation was reduced from 3L_o to 0.3L_o, the apparent hydrodynamic thickness (R) decreased monotonically to values R ≪ R_H. Physically, this indicates that the “slip plane” moved progressively closer to the solid surfaces with decreasing surface–surface separation. This was accompanied by augmentation of the effective viscosity by a factor of up to approximately 5, indicating somewhat diminished permeability of solvent through the overlapping polymer layers. Similar results hold for the flow through surface-anchored polymers in a good solvent. It is interesting to note the strong stretching of densely end-grafted polymers in a theta solvent. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2961–2968, 1997     

The reaction-annihilator distribution and the nonholonomic Noether theorem for lifted actions

We consider nonholonomic systems with linear, time-independent constraints subject to positional conservative active forces. We identify a distribution on the configuration manifold, that we call the reaction-annihilator distribution ℜ°, the fibers of which are the annihilators of the set of all values taken by the reaction forces on the fibers of the constraint distribution. We show that this distribution, which can be effectively computed in specific cases, plays a central role in the study of first integrals linear in the velocities of this class of nonholonomic systems. In particular we prove that, if the Lagrangian is invariant under (the lift of) a group action in the configuration manifold, then an infinitesimal generator of this action has a conserved momentum if and only if it is a section of the distribution ℜ°. Since the fibers of ℜ° contain those of the constraint distribution, this version of the nonholonomic Noether theorem accounts for more conserved momenta than what was known so far. Some examples are given.      

Modeling slow deformation of polygonal particles using DEM

We introduce two improvements in the numerical scheme to simulate collision and slow shearing of irregular particles. First, we propose an alternative approach based on simple relations to compute the frictional contact forces. The approach improves efficiency and accuracy of the Discrete Element Method (DEM) when modeling the dynamics of the granular packing. We determine the proper upper limit for the integration step in the standard numerical scheme using a wide range of material parameters. To this end, we study the kinetic energy decay in a stress controlled test between two particles. Second, we show that the usual way of defining the contact plane between two polygonal particles is, in general, not unique which leads to discontinuities in the direction of the contact plane while particles move. To solve this drawback, we introduce an accurate definition for the contact plane based on the shape of the overlap area between touching particles, which evolves continuously in time.     

FORCE FIELDS ON INVISCID,SLENDER, ANNULAR LIQUID JETS

Regular perturbation expansions are used to analyse the fluid dynamics of unsteady, inviscid, slender, thin, incompressible (constant density), axisymmetric, upward and downward, annular liquid jets subjected to non-homogeneous, conservative body forces when both the annular jets are very thin and the gases enclosed by and surrounding the jet are dynamically passive. Both inertia- and capillarity-dominated annular jets are considered. It is shown that, for inertia-dominated jets, closure of the leading-order equations is achieved at second order in the perturbation parameter, which is the slenderness ratio, whereas closure is achieved at first order for capillarity-dominated jets. The steady leading-order equations are solved numerically by means of both an adaptive finite difference method which maps the curvilinear geometry of the jet onto a unit square and a fourth-order-accurate Runge–Kutta technique. It is shown that the fluid dynamics of steady, annular liquid jets is very sensitive to the Froude and Weber numbers and nozzle exit angle in the presence of non-homogeneous, conservative body forces. For upward jets with inwardly or axially directed velocities at the nozzle exit the effect of the non-homogeneous, conservative body forces is to increase the leading-order axial velocity component, decrease the jet's mean radius and move the stagnation point downstream. For downward jets with radially outward velocity at the nozzle exit the axial velocity component decreases monotonically as the magnitude of the non-homogeneous, conservative body forces is increased.     

Relaxation of a dislocation in a nanocrystallite

Experimental studies of dislocations in nanoparticles are just beginning. The corresponding theoretical models are still lacking. In this context, the author analyzes relaxation of a dislocation in a nanoparticle. Mechanistically, this process is considered to occur primarily via dislocation drift induced by the stress-related image forces. Elementary dislocation displacements include the formation of a kink at one of the sides of the dislocation line, its diffusion along this line, and annihilation at the opposite side. For this mechanism, the dependence of the time of dislocation disappearance on the nanoparticle size has been identified.     

Semi-discrete breather in a helicoidal DNA double chain-model

The nonlinear dynamics of DNA molecular chain is studied for longitudinal and transversal motions through a new discrete helicoidal zigzag model with four degrees of freedom. We take into account the Stokes and hydrodynamical viscous forces. In the semi-discrete approximation, we show that the coupled nonlinear partial differential equations for the longitudinal and transversal out-of-phase motions can be reduced to the nonlinear Schrödinger equation with complex coefficients, allowing analytical breather soliton solution. We found analytically as well as numerically that increasing the damping constant reduces the amplitude and increases the width of the soliton. When the zigzag angle decreases, the height of the soliton increases, but its width remains constant. The linear stability analysis of the system is performed. The growth rate of the instability and the instability regions are discussed as the functions of damping constant, zigzag angle and system parameters.     

双侧下颌支矢状劈开截骨术后患者可施加合适咬合力的数值研究

双侧下颌支矢状劈开截骨术在临床手术中广泛用于治疗缩颌、凸颌和颌面不对称患者的颌面畸形症状。本文用数值方法研究双侧下颌支矢状劈开截骨术并前移下颌骨后患者可施加的合适咬合力。首先,用缩颌患者的CT断层扫面数据建立下颌骨、关节盘、关节窝和相关软组织的高度几何相似性的几何模型;然后,用有限元模型模拟双侧下颌支矢状劈开截骨术后患者的咬合过程。通过分析发现,术后关节盘上的位移处于正常的范围,而应力却远远超过正常范围,因此,将应力因素作为确定术后患者可施加的合适咬合力的标准。当施加正常咬合力的25%时,关节盘上的应力分布和术前没有显著性差异,同时下颌骨上的应力水平也处于正常范围。     

Fog and dense gas disrupt mosquito flight due to increased aerodynamic drag on halteres

Chemical insecticide foggers have long been used to control mosquito populations and reduce the spread of malaria, West Nile virus, and dengue fever. In this study, we show that simple fogs of water droplets, devoid of chemicals, are effective at obstructing the flight of Anopheles freeborni mosquitoes. Using high-speed video, we film the flight of mosquitoes in denser-than-air fluids such as fogs produced by household humidifiers and heavy gas. In gases with more than twice the density of air, mosquitoes cannot maintain flight stability, but pitch and roll uncontrollably until they fall to the ground. We here show that the increased drag of denser-than-air flight environments is sufficient to render a mosquito׳s gyroscopic sensors and wingbeat controllers, their halteres, ineffective. Anomalous drag forces are estimated with steady and unsteady drag analyses. We glue masses of 10 ng to each haltere, equivalent to 0.0005% the mass of the mosquito. Mosquitoes with such a minor treatment executed flight patterns, similar to mosquitoes in fog, indicating a mosquito׳s haltere are highly tuned to aerodynamic properties of normal air, making them sensitive to contaminants. The failure of mosquito flight in fog reveals potential new methods for mosquito control that do not require insecticide-laced particles.