Spherical Endcaps Research Articles

Discovery of Y-Shaped Supramolecular Polymers in a Self-Assembling Peptide Amphiphile System.

Supramolecular polymers (SPs) formed by self-assembly of peptide-based molecular units assume a variety of interesting one-dimensional (1D) morphologies. While the morphological complexity and phase behavior of self-assembling peptide conjugates bear some resemblance to those of low-molecular-weight and macromolecular surfactants, Y-junctions, or three-way connected constructs, a topological defect observed in traditional surfactants has not been identified, likely due to the intolerance of defective packing by the strong, associative interactions afforded by the peptide segments. Here we report our discovery of branched SPs with Y-junctions and occasionally enlarged spherical end-caps formed by micellization of a ferrocene-based peptide amphiphile in water. Our results suggest that the incorporation of two ferrocenes into the amphiphile design is key to ensure the formation of branched SPs. We hypothesize that the complex interplay of internal interactions limits the effective propagation of hydrogen bonding within the assemblies and, consequently, creates fragmented β-sheets that are more tolerant for supramolecular branching. Given the redox sensitivity of the ferrocene units, sequential addition of reductants and oxidants to the solution led the assemblies to reversibly transform between branched SPs and spherical aggregates.

Advanced Rendering of Line Data with Ambient Occlusion and Transparency.

3D Lines are a widespread rendering primitive for the visualization of data from research fields like fluid dynamics or fiber tractography. Global illumination effects and transparent rendering improve the perception of three-dimensional features and decrease occlusion within the data set, thus enabling better understanding of complex line data. We present an efficient approach for high quality GPU-based rendering of line data with ambient occlusion and transparency effects. Our approach builds on GPU-based raycasting of rounded cones, which are geometric primitives similar to truncated cones, but with spherical endcaps. Object space ambient occlusion is provided by an efficient voxel cone tracing approach. Our core contribution is a new fragment visibility sorting strategy that allows for interactive visualization of line data sets with millions of line segments. We improve performance further by exploiting hierarchical opacity maps.

Analytical modeling of micelle growth. 4. Molecular thermodynamics of wormlike micelles from ionic surfactants: Theory vs. experiment

HypothesesThe aggregation number and length of spherocylindrical (rodlike, wormlike) micelles in solutions of an ionic surfactant and salt can be predicted knowing the molecular parameters and the input concentrations of the species. This can be achieved by upgrading the quantitative molecular thermodynamic model from the previous parts of this series with an expression for the electrostatic component of micelle scission energy that is the excess free energy of the spherical endcaps with respect to the cylindrical part of the micelle. TheoryThe thermodynamics of micellization is extended to the case of multicomponent system, which may contain several surfactants (both ionic and nonionic) and salts, taking into account the effect of counterion binding in the Stern layer on the micellar surface. Furthermore, the considerations are focused on a system that consists of single ionic surfactant plus salt. FindingsExcellent agreement was achieved between the theoretical model and experimental data for wormlike micelles from anionic and cationic surfactants at various concentrations of salt and temperatures. In accord with the experimental observations, at high salt concentrations, the model predicts loss of chemical equilibrium between the endcaps and cylindrical part of the wormlike micelles, which implies transition to self-assemblies of other, e.g. branched, morphology or the onset of crystallization and phase separation.

Locomotion of a rotating cylinder pair with periodic gaits at low Reynolds numbers

We consider the periodic gaits of a microswimmer formed by two rotating cylinders, placed apart at a fixed width. Through a combination of theoretical arguments and numerical simulations, we derive semi-analytic expressions for the system’s instantaneous translational and rotational velocities, as a function of the rotational speeds of each cylinder. We can then integrate these relations in time to find the speed and efficiency of the swimmer for any imposed gait. Here, we focus particularly on identifying the periodic gaits that lead to the highest efficiency. To do so, we consider three stroke parameterizations in detail: alternating strokes, where only one cylinder rotates at a time; tilted rectangle strokes, which combine co- and counter-rotation phases; and smooth strokes represented through a set of Fourier series coefficients. For each parameterization, we compute maximum efficiency solutions using a numerical optimization approach. We find that the parameters of the global optimum, and the associated efficiency value, depend on the average mechanical input power. The globally optimal efficiency asymptotes toward that of a steadily counter-rotating cylinder pair as the input power increases. Finally, we address a possible three-dimensional (3D) extension of this system by evaluating the efficiency of a counter-rotating 3D cylinder pair with spherical end caps. We conclude that the counter-rotating cylinder pair combines competitive efficiency values and high versatility with simplicity of geometry and actuation, and thus forms a promising basis for engineered microswimmers.

On One Imperfection Estimation Method for Thin Shell Buckling in the Design Code RCC-MR

The thin shell design code RCC-MR is used for sodium-cooled fast breeder reactor components operating at high temperatures. Thin shells from such applications can be designed using linear elastic buckling analysis, following procedures given in RCC-MR. For human safety, such procedures can and should be examined by the broader scientific community. Among such procedures, RCC-MR provides three alternative methods to quantify an imperfection value; and that value is used in subsequent calculations to determine safe loads. Of these methods, the third seems potentially nonconservative for some situations. Here, we examine that third method using detailed numerical examples. These examples, found by trial and error, are the main contribution of this paper. The first example is a nonuniform cylindrical shell closed with a spherical endcap under external pressure. The second is a cylinder with an ellipsoidal head under internal pressure. The third is an L-shaped pipe with an end load. In all three cases, the new computed imperfection quantity is found to be surprisingly small compared to the actual value used for computations (e.g., 25 times smaller), and in two cases, the result is insensitive to the actual imperfection. We explain how the three examples “trick” the imperfection quantification method in three different ways. We suggest that this imperfection quantification method in RCC-MR should be re-examined. The primary value of our paper lies not in new mechanics, but in identifying unexpected ways in which a particular step in shell design using RCC-MR could be potentially nonconservative.

Analytical modeling of micelle growth. 2. Molecular thermodynamics of mixed aggregates and scission energy in wormlike micelles

HypothesesQuantitative molecular-thermodynamic theory of the growth of giant wormlike micelles in mixed nonionic surfactant solutions can be developed on the basis of a generalized model, which includes the classical “phase separation” and “mass action” models as special cases. The generalized model describes spherocylindrical micelles, which are simultaneously multicomponent and polydisperse in size. TheoryThe model is based on explicit analytical expressions for the four components of the free energy of mixed nonionic micelles: interfacial-tension, headgroup-steric, chain-conformation components and free energy of mixing. The radii of the cylindrical part and the spherical endcaps, as well as the chemical composition of the endcaps, are determined by minimization of the free energy. FindingsIn the case of multicomponent micelles, an additional term appears in the expression for the micelle growth parameter (scission free energy), which takes into account the fact that the micelle endcaps and cylindrical part have different compositions. The model accurately predicts the mean mass aggregation number of wormlike micelles in mixed nonionic surfactant solutions without using any adjustable parameters. The endcaps are enriched in the surfactant with smaller packing parameter that is better accommodated in regions of higher mean surface curvature. The model can be further extended to mixed solutions of nonionic, ionic and zwitterionic surfactants used in personal-care and house-hold detergency.

Bird Strike Modeling in Fiber-Reinforced Polymer Composites

The present paper describes a numerical modeling approach to predict impact resistance and residual Shear Strength After Impact (SSAI) of fiber reinforced polymer composites subjected to bird strike loading. An improved damage mechanics based on material model, previously developed by the authors, is combined with an equation of state to simulate the progressive failure in composite aerostructures subjected to bird strike loading. A series of bird strike impacts on flat panels fabricated from low cost woven glass composite materials are used to validate the material model for practical composite component applications. A numerical study on the residual SSAI of a typical composite shear web is also presented. The panels are modelled with shell elements only. The proposed material model formulation accounts for the strain rate enhancement to strength and shear nonlinearities observed in composite materials. A hydrodynamic model for the bird, based on 90% water and 10% air, is derived to represent the behavior of the bird for all impact scenarios considered. The bird is heterogeneous in nature. However, a uniform material behavior is assumed with a geometry based on a 2:1 length to diameter ratio with a cylindrical body and spherical end caps using Lagrangian mesh. Appropriate contact definitions are used between the bird and the composite panel. The simulations results are compared to experimental results and conclusions drawn.

Modeling high frequency broadband acoustic fields inside rectangular and cylindrical enclosures using an energy-intensity boundary element method

Accurate prediction of high frequency broadband acoustic fields inside enclosures with curved boundaries typically requires time consuming frequency-by-frequency numerical techniques. A quick solution is developed for general enclosure shapes using an energy-intensity boundary element method, previously tested for rectangular geometries and now extended to cylinders with flat or spherical endcaps. Derived from first principles, which are reviewed, the approach uses uncorrelated spreading energy-intensity boundary sources to directly solve for the steady-state mean-square pressures. The enclosure boundary is discretized into radiating panels that account for interior energy transfer and satisfy prescribed reflection and absorption boundary conditions. Half-space orthogonal spherical harmonics serve as basis functions to emulate both diffuse and specular reflections. Panel interactions are calculated by an energy-accurate quadrature technique and studied for curved boundaries. Computationally intensive benchmark solutions are developed for verification. A fully correlated Helmholtz solution is derived for the cylindrical enclosure using a novel internal scattering approach to calculate high frequency pressure, and numerically integrated over a third-octave band. Comparisons between the fully correlated solution and the energy method for enclosures of various aspect ratios reveal excellent agreement. Simulations are also presented contrasting interesting behavioral differences between diffuse and specular reflection fields.

Model of cylindrical micelles with different endcaps

ABSTRACTThe system of alcohol (C8OH) and hexadecyl trimethyl ammonium bromide (CTAB) was studied by molecular dynamics simulation, and the cylindrical (or rod-like) micelles with different endcaps were obtained. The simulation results presented the different terminal structures of the cylindrical (rod-like) micelles. According to the critical packing parameters of the micellar stability theory, the microscopic structures of cylindrical (or rod-like) micelles with different endcaps were analyzed. The shorter rod-like micelle was constituted by the cylindrical body and two swelling spherical endcaps, while the longer cylindrical (or rod-like) micelle had two spherical crown endcaps less than the hemisphere. The models of the cylindrical (rod-like) micelles were presented in detail based on the simulation results and the micellar stability theory.

Nematic-smectic transition of parallel hard spheroellipsoids.

Spheroellipsoids are truncated ellipsoids with spherical end caps. If gradients are assumed to change smoothly at the junction of body and cap, the truncation height z0 determines the geometry uniquely. The resulting model particle has only two shape parameters, namely, the aspect ratio c/a of the basic ellipsoid and the cutoff z0/a. These two parameters can be tuned to yield a continuous transformation between a pure ellipsoid and a spherocylinder. Since parallel hard spherocylinders display a nematic-smectic A phase transition, while ellipsoids do not, the influence of the particle shape on the possibility of a smectic phase may be investigated. A density functional analysis is used to detect the dividing line, in the (c/a, z0/a) plane, between the presence and absence of the N-S transition. Since spheroellipsoids may be useful as generic model particles for anisotropic molecules, we provide a computationally efficient overlap criterion for a pair in a general, non-parallel configuration.

How a Viscoelastic Solution of Wormlike Micelles Transforms into a Microemulsion upon Absorption of Hydrocarbon: New Insight

In this article, we investigate the effect of hydrocarbon addition on the rheological properties and structure of wormlike micellar solutions of potassium oleate. We show that a viscoelastic solution of entangled micellar chains is extremely responsive to hydrocarbons-the addition of only 0.5 wt % n-dodecane results in a drastic drop in viscosity by up to 5 orders of magnitude, which is due to the complete disruption of micelles and the formation of microemulsion droplets. We study the whole range of the transition of wormlike micelles into microemulsion droplets and discover that it can be divided into three regions: (i) in the first region, the solutions retain a high viscosity (∼10-350 Pa·s), the micelles are entangled but their length is reduced by the solubilization of hydrocarbons; (ii) in the second region, the system transitions to the unentangled regime and the viscosity sharply decreases as a result of further micelle shortening and the appearance of microemulsion droplets; (iii) in the third region, the viscosity is low (∼0.001 Pa·s) and only microemulsion droplets remain in the solution. The experimental studies were accompanied by theoretical considerations, which allowed us to reveal for the first time that (i) one of the leading mechanisms of micelle shortening is the preferential accumulation of the solubilized hydrocarbon in the spherical end caps of wormlike micelles, which makes the end caps thermodynamically more favorable; (ii) the onset of the sharp drop in viscosity is correlated with the crossover from the entangled to unentangled regime of the wormlike micellar solution taking place upon the shortening of micellar chains; and (iii) in the unentangled regime short cylindrical micelles coexist with microemulsion droplets.

Cylindrical Cellular Geometry Ensures Fidelity of Division Site Placement in Fission Yeast

Successful cytokinesis requires proper assembly of the contractile actomyosin ring, its stable positioning on the cell surface and proper constriction. Over the years, many of the key molecular components and regulators of the assembly and positioning of the actomyosin ring have been elucidated. Here we show that cell geometry and mechanics play a crucial role in the stable positioning and uniform constriction of the contractile ring. Contractile rings that assemble in locally spherical regions of cells are unstable and slip towards the poles. By contrast, actomyosin rings that assemble on locally cylindrical portions of the cell under the same conditions do not slip, but uniformly constrict the cell surface. The stability of the rings and the dynamics of ring slippage can be described by a simple mechanical model. Using fluorescence imaging, we verify some of the quantitative predictions of the model. Our study reveals an intimate interplay between geometry and actomyosin dynamics, which are likely to apply in a variety of cellular contexts.

Transformation acoustics: Theory, ray‐tracing, and finite element simulations.

Norris’ theory of transformation acoustics enables the realization of pentamode acoustic materials having anisotropic density and finite mass. Two additional extensions of the theory are considered, with a view toward demonstrating feasibility for practical applications. First, specializations of the theory developed by Norris [“Acoustic cloaking theory,” Proc. R. Soc. London, Ser. A 464, 2411–2434 (2008)] are considered in order to develop transformations corresponding to pentamode acoustic metamaterials with specified functional forms (constant or powerlaw) for density and stiffness. Ray‐tracing and finite element simulations of wave propagation through such pentamode acoustic media are presented. Next, the design of acoustic materials for objects composed of simple geometric shapes (e.g., a cylinder with spherical endcaps) is considered. It is shown that certain classes of transformations are well‐suited for the design of such shapes and validate the concept with finite element simulations.

Angularly resolved light scattering from aerosolized spores: observations and calculations

Angularly resolved elastic light scattering patterns from individual aerosolized Bacillus subtilis spores were qualitatively compared with simulations. Two-dimensional angular optical scattering patterns of the spores were collected for polar scattering angles varying from approximately 77 degrees to 130 degrees and azimuthal angles varying from 0 degrees to 360 degrees . Computations were performed with single T-matrix formalism by simulating a spore with three different particle shapes: (1) a finite-length cylinder with spherical end caps, (2) a spheroid, and (3) two spheres in contact. Excellent agreement between computation and measurement was found for the finite-length cylinder with spherical end caps, poorer agreement was found for the spheroids, and the poorest agreement was for the two spheres in contact.

Effect of Mixing on the Morphology of Cylindrical Micelles

Increasing the spontaneous curvature of an amphiphile can lead to a first-order morphology transition from threadlike micelles to a branched network. The two morphologies were linked to entropy-driven topological defects; networks are dominated by Y-junctions, while linear threadlike structures are dominated by spherical end-caps. In this paper we investigate the effect of mixing on the morphological transitions in nonionic amphiphilic systems. We find that mixed equilibrium structures are obtained within seconds; these mixed cylindrical structures display comparable numbers of end-caps and branch points, resulting in a novel 'short armed' branched (SAB) morphology. Quite surprisingly, the probability of either defect (end-caps or branch points) is independent of composition, so that neither a first-order nor a second-order morphological transition is observed. A possible explanation may be local demixing of the two amphiphilic components, which adds a degree of freedom and thus enables the formation of a unique morphology that cannot be obtained in single-component systems. We further find that within a relatively large composition range phase equilibrium exists between vesicles, SAB micelles, and spherical micelles.

Reply to “Comment on ‘Morphology of Silicon Nitride Grown from a Liquid Phase’”

In their comment on the authors paper, Kitayama et. al. suggested that the weighted mean curvature method should have been used to obtain surface chemical potential. Their results are correct, but only for crystals that have a flat end. Since the grains of {beta}-Si{sub 3}N{sub 4} in the authors observation, as well as others reported in the literature, are not fully faceted and do not have flat ends, their result cannot be applied to those cases. They are certainly not useful for treating surface morphology that has undulations. To allow a more general discussion not restricted to grains with flat ends, the authors have derived the surface potential for a rod-shaped crystal having spherical end caps and a circular cross section.

Progress in hybrid finite-element/propagation tool modeling of scattering from objects in underwater waveguides

A steady-state 3D finite-element software called FESTA (Finite-Element STructural Acoustics), is being developed at the NATO Undersea Research Centre. The code is geared towards a variety of applications in underwater acoustics, such as multistatic scattering from localized inhomogeneities, scattering across interfaces between fluids and/or solids, and multistatic scattering from single and multiple fluid-loaded elastic targets. One issue of importance to researchers in underwater acoustics is the trade-off between full 3D models and thin-shell theory. To address this issue, FESTA results are compared to results from thin-shell scattering codes for cylindrical bodies with spherical endcaps. Another part of the work focuses on the integration of the finite-element tool with underwater propagation tools for the computation of multistatic scattering from targets buried, partially buried or proud inside shallow-water waveguides. To achieve this, FESTA is coupled to the MIT underwater propagation tool OASES. One method of interfacing FESTA to OASES is based on an environment-independent characterization of the target via in vacuo response matrices. Recent results from response matrix computations are presented and trade-offs of this method are discussed.

Axisymmetric slosh frequencies of a liquid mass in a circular cylinder

Spectral eigenvalue methods along with some lower-dimensional techniques are used to determine the natural frequencies of a liquid slug in a circular tube. The contact lines are either pinned or governed by a slip coefficient assumed small. Corresponding physical experiments are conducted for a borosilicate glass tube and a treated water slug. Gravitational and viscous effects are neglected for the analyses. The spectral results agree well with a simple spherical end cap approximation (zero dimensional) for large aspect ratio slugs and with a membrane approximation (one dimensional) for small aspect ratios. The experimental observations for different aspect ratios agree well with the predictions, although the gravity, viscosity and/or slip are neglected in the analyses.

Reconstruction of acoustic radiation from vibrating objects in a half space using hybrid nearfield acoustical holography

Hybrid nearfield acoustical holography (NAH) [Wu, J. Acoust. Soc. Am. 113, 2252 (2003)] is utilized to reconstruct the vibro-acoustic fields generated by vibrating structures in half space. These hybrid formulations are derived from a modified Helmholtz equation least-squares method, where the field acoustic pressure is expanded in terms of both outgoing and incoming spherical waves, and the Helmholtz integral formulations implemented by the boundary element method (BEM). To overcome the ill-conditioning difficulties in the resultant matrix equations, regularization techniques such as the method of Tikhonov and generalized cross validation are employed. The main advantage of this hybrid approach is that satisfactory reconstruction can be obtained with relatively few acoustic pressure measurements taken over a conformal surface around the source. This is because a large portion of the input data is regenerated by the modified HELS, but not actually measured. Hence, the efficiency of reconstruction is enhanced. If the same number of measurements is used in an inverse BEM code, the reconstructed vibro-acoustic quantities on the source surface may be distorted. Numerical examples of a dilating and an oscillating sphere and a cylinder with spherical endcaps in half space are demonstrated. [Work supported by NSF.]

The detection of surface vibrations from interior acoustical pressure

We consider the problem of detecting the source of acoustical noise inside thecabin of a midsize aircraft from measurements of the acoustical pressure fieldinside the cabin. Mathematically this field satisfies the Helmholtz equation. Inthis paper we consider the three-dimensional case. We show that anyregular solution of this equation admits a unique representation by asingle-layer potential, so that the problem is equivalent to the solutionof a linear integral equation of the first kind. We study uniqueness ofreconstruction and obtain a sharp stability estimate and convergence rates forsome regularization algorithms when the domain is a sphere. We havedeveloped a boundary element code to solve the integral equation. We reportnumerical results with this code applied to three geometries: a sphere, acylinder with spherical endcaps and a cylinder with a floor modellingthe interior of an aircraft cabin. The exact test solution is given by apoint source exterior to the surfaces with about 1% random noise added.Regularization methods using the truncated singular value decomposition withgeneralized cross validation and the conjugate gradient (cg) method with astopping rule due to Hanke and Raus are compared. An interesting feature ofthe three-dimensional problem is the relative insensitivity of the optimalregularization parameter (number of iterations) for the cg method to thewavenumber and the multiplicity of the singular values of the integral operator.