Fixed Surface Area Research Articles

Global minimizers for the doubly-constrained Helfrich energy: the axisymmetric case

Since the pioneering work of Canham and Helfrich, variational formulations involving curvature-dependent functionals, like the classical Willmore functional, have proven useful for shape analysis of biomembranes. We address minimizers of the Canham–Helfrich functional defined over closed surfaces enclosing a fixed volume and having fixed surface area. By restricting attention to axisymmetric surfaces, we prove the existence of global minimizers.

5:1의 형상비를 갖는 사각덕트에서 직조 스크린 리입(rib)이 열전달과 마찰계수에 미치는 영향

직조 금속 스크린 리브(rib) 이 바닥에 설치된 사각 덕트에서 열전달과 유체유동의 압력강하를 측정하기 위해 실험적 연구를 수행하였다. 시험부의 치수는 200 mm(W) <TEX>${\times}$</TEX> 40 mm(H) <TEX>${\times}$</TEX> 712 mm(L)이고 수력직경은 66.6 mm이다. 입구영역에는 1.72m 길이의 가열되지 않은 동일한 치수의 채널을 설치하였다. 메쉬가 다른 4가지의 직조금속 스크린 리브에 대해 측정하였다. 그리고 비교를 위해 일체형 리브에 대해서도 측정하였다. 국부 열전달 계수의 측정에는 스테인레스 강제 포일(foil) 히터와 T형 열전대률 이용하였다. 레이놀즈 수는 23,000에서 58,000의 범위이다. 덕트의 수력직경(<TEX>$D_h$</TEX>)에 대한 직조 금속 리브의 높이(e)의 비(<TEX>$e/D_h$</TEX>)는 0.075 이고 리브 간격(p)과 높이의 비(p/e)는 10이다. 실험 결과 메쉬가 없는 일체형 리입에서 가장 누셀트 수와 마찰계수가 컷다.

Investigations of the reduction of NO to N 2 by reaction with Fe

The paper presents the results of the investigation of nitric oxide reduction by its reaction with metallic iron, within the temperature range of 750–1200 °C. Experiments were carried out in a one-dimensional tubular flow reactor externally heated in an electrical furnace. The spherical and cylindrical iron samples of well-defined and fixed surface area were placed in the center of the reactor. Mixtures NO/N 2, NO/O 2/N 2, NO/CO 2/N 2 of different molar compounds fractions were continuously fed into the reactor. The surfaces and cross-sections of partly oxidized iron samples were observed using a scanning microscope. The rate of nitric oxide reduction in the first stage of iron oxidization was measured. The obtained values lie between those presented in the literature and measured in the fluidized bed reactor and thermogravimetrically. A very strong influence of oxygen but a very weak one of carbon dioxide on the efficiency of NO reduction was observed within the investigated range of temperature.

Design Optimization of a Bidirectional Microswimming Robot Using Giant Magnetostrictive Thin Films

This paper presents a bidirectional optimization method on a wireless microswimming robot. The robot is developed based on fin beating propulsion employing two giant magnetostrictive thin films for left and right fins. An innovative drive approach, using separate second-stage resonance frequencies of the left and right fins to generate right and left thrusts, is proposed and implemented on a bidirectional microswimming robot prototype. Dynamic model of the proposed microrobot has been derived based on theoretical analysis. A discrete variate method for optimizing left fin configuration is proposed under the constraints of fixed surface area and sufficient fin end strength, and a genetic algorithms method for optimizing right fin configuration is employed under constraints of symmetry and linearity of bidirectional swimming. Simulation and experimental results have demonstrated that bidirectional swimming performance of the robot is greatly improved with low driving frequency and a large range of swimming speed in both directions.

Accurate Coarse-Grained Modeling of Red Blood Cells

We develop a systematic coarse-graining procedure for modeling red blood cells (RBCs) using arguments based on mean-field theory. The three-dimensional RBC membrane model takes into account the bending energy, in-plane shear energy, and constraints of fixed surface area and fixed enclosed volume. The coarse-graining procedure is general, it can be used for arbitrary level of coarse-graining and does not employ any fitting parameters. The sensitivity of the coarse-grained model is investigated and its behavior is validated against available experimental data and in dissipative particle dynamics (DPD) simulations of RBCs in capillary and shear flows.

Microstructural evolution of Mg–Al–Ca–Sr alloy during creep

To provide new insight into microstructural development during creep, sequential EBSD (electron backscatter diffraction) orientation maps were obtained from fixed surface areas at intervals in creep tests of a high-pressure die-cast Mg–8.5Al–1Ca–0.3Sr alloy. Samples were tested at 200 °C at various stress levels to achieve power-law creep behavior. In all specimens, steady-state creep was marked by the formation of tension twins. At intermediate stress levels, specimen failure was initiated by the formation of defects at boundaries with high crystallographic misorientation. However, at high stress levels, the failure mechanism was assisted by the crack formation at interdendritic boundaries with low crystallographic misorientation.

Electron Backscatter Diffraction Mapping of Microstructural Evolution of Pure Magnesium during Creep

To provide new insight into microstructural development during creep, sequential electron backscatter diffraction (EBSD) orientation maps were obtained from fixed surface areas during interrupted creep tests of extruded pure magnesium. Samples were tested under two distinctly different conditions, i.e., low-temperature power-law creep and high-temperature power-law creep. Three aspects of microstructural evolution during creep were observed. In both specimens, transient creep was marked by the elimination of tension twins formed during the extrusion process. As steady-state creep rates were obtained, both specimens exhibited an ever-decreasing contribution by basal slip accompanied by an ever-increasing contribution by prismatic slip. In the low-temperature specimen, prismatic slip was manifested by the formation of a network of new fine subgrains along original grain boundaries, resulting in a bimodal grain size distribution. However, the high-temperature specimen developed linear prismatic slip lines while maintaining its original grain size.

Template Adaptability Is Key in the Oriented Crystallization of CaCO3

In CaCO3, biomineralization nucleation and growth of the crystals are related to the presence of carboxylate-rich proteins within a macromolecular matrix, often with organized beta-sheet domains. To understand the interplay between the organic template and the mineral crystal it is important to explicitly address the issue of structural adaptation of the template during mineralization. To this end we have developed a series of self-organizing surfactants (1-4) consisting of a dodecyl chain connected via a bisureido-heptylene unit to an amino acid head group. In Langmuir monolayers the spacing of these molecules in one direction is predetermined by the hydrogen-bonding distances between the bis-urea units. In the other direction, the intermolecular distance is determined by steric interactions introduced by the side groups (-R) of the amino acid moiety. Thus, by the choice of the amino acid we can systematically alter the density of the surfactant molecules in a monolayer and their ability to respond to the presence of calcium ions. The monolayer films are characterized by surface pressure-surface area (pi-A) isotherms, Brewster angle microscopy, in-situ synchrotron X-ray scattering at fixed surface area, and also infrared reflection absorption spectroscopy (IRRAS) of films transferred to solid substrates. The developing crystals are studied with scanning and transmission electron microscopy (SEM, TEM), selected area electron diffraction (SAED), and crystal modeling. The results demonstrate that although all compounds are active in the nucleation of calcium carbonate, habit modification is only observed when the size of the side group allows the molecules to rearrange and adapt their organization in response to the mineral phase.

Inverted catenoid as a fluid membrane with two points pulled together

Under inversion in any (interior) point, a catenoid transforms into a deflated compact geometry which touches at two points (its poles). The catenoid is a minimal surface and, as such, is an equilibrium shape of a symmetric fluid membrane. The conformal symmetry of the Hamiltonian implies that inverted minimal surfaces are also equilibrium shapes. However, they will exhibit curvature singularities at their poles. Such singularities are the geometrical signature of the external forces required to pull the poles together. These forces will set up stresses in the inverted shapes. Tuning the force corresponds geometrically to the translation of the point of inversion. For any fixed surface area, there will be a maximum force. The associated shape is a symmetric discocyte. Lowering the external force will induce a transition from the discocyte to a cup-shaped stomatocyte.

Supramolecular Structures Generated by a p‐tert‐Butylphenyl‐amide Derivative of Cholic Acid: From Vesicles to Molecular Tubes

The formation of supramolecular structures initiated by a p-tert-butylphenyl-amide derivative of cholic acid is investigated. The initial spherical vesicles, with a rather low effective bending constant, collapse into necklaces that self-transform into tubules of small diameter. Finally, molecular tubes are generated (see figure). During the process, the geometrical constraints of fixed surface area and fixed enclosed volume are obeyed.

The effect of inverted micelles adsorbed on different metals on the hydrolysis of methyl salicylate and ethyl acetoacetate

Hydrolysis of methyl salicylate was carried out on inverted micelles adsorbed on copper. The initial rate of hydrolysis was found to be a linear function of the surfactant concentration and copper surface area. However, the initial rate was found to be linear only at low surfactant concentrations for a fixed surface area of copper, and reached a maximum at higher concentrations. Cetyltrimethylammonium bromide (CTAB) was found to be a better catalyst both in the ordinary micelle and in its inverted form than the corresponding Hyamine surfactant. The effect of different metals on the initial rate of ethyl acetoacetate hydrolysis was investigated. An enhanced rate of hydrolysis was observed on the selected metals used (Al, Cu. Pb and Sn) and the magnitude of the rate enhancement was observed to be dependent on the potential of zero charge (pzc) of these metals.

Numerical analysis of latent heat thermal energy storage system

Abstract This paper presents a comparative study of the total melting time of a phase change material (PCM) packed in three containers of different geometric configurations, viz. rectangular, cylindrical and cylindrical shell, having the same volume and surface area of heat transfer. Employing a slightly modified enthalpy method, which enables decoupling of the temperature and liquid fraction fields, the governing equation for one dimensional isothermal phase change is discretized using the Crank–Nicholson finite difference scheme. While the resulting system of algebraic equations for temperature is solved using the Thomas algorithm, the liquid fraction field is updated explicitly using the currently known temperature field. The results are presented for different masses of PCM filling the containers and inlet temperature of the heat transfer fluid (HTF). On the basis of detailed discussion of these results, it is concluded that for the same mass of PCM and surface area of heat transfer, cylindrical shell containers take the least time for equal amounts of energy storage, and this geometric effect is more pronounced with an increase in the mass of the PCM. It is also found that for cylindrical shell containers, an increase in the inlet temperature of the HTF from its lower range of values results in a drastic decrease in energy storage time, while this effect of inlet temperature of the HTF diminishes sharply at higher and higher values. Further, it is observed that as the mass of the PCM in the cylindrical shell container having a fixed surface area of heat transfer increases, the reduction in total melting time due to an increase in the inlet temperature of the HTF becomes more and more pronounced.

Experimental study of lapping and electropolishing of tungsten carbides

Lapping and electropolishing (EP) experiments for tungsten carbide blocks were executed. The effectiveness of the lapping experiment is evaluated in terms of the material removal rate, the surface roughness, and wear of the workpiece. The material removal rate describes the thickness removal of the workpiece under a fixed surface area. Wear describes a microscopic study of the wear track. The results show that the material removal and surface roughness increase as the grain size of the abrasive increases. Four main wear mechanisms -- abrasive wear, fracture, adhesive wear and scratch -- are observed during the lapping of tungsten carbide using silicon carbide abrasive. In the electropolishing experiment, four different machining characteristics -- sub-electropolishing, crack, electropolishing, and pitting -- can be analyzed as the applied current is increased. Although material removal is close to Faraday’s law during electropolishing, it disagrees with Faraday’s law after 400 s of sub-electropolishing.

Urea Coordinated Titanium Trichloride TiIII[OC(NH)2]6Cl3: A Single Molecular Precursor Yielding Highly Visible Light Responsive TiO2 Nanocrystallites

A coordination complex, Ti(III)[OC(NH2)2]6Cl3, was first synthesized via reacting hot alcoholic solutions of TiCl3 and urea, which was subsequently employed as a molecular precursor for nanocrystalline TiO2 via thermal decomposition. Fourier transform IR spectroscopy confirmed C=O-->Ti coordination bond formation, while Rietveld refinement revealed a hexagonal crystal structure (space group: Pc1) for the complex with a = b = 16.438(4) A, c = 15.423(3) A, alpha = beta = 90 degrees , gamma = 120 degrees , and V = 3608.9(13) A3. Thermal decomposition and phase evolution processes of the complex were investigated in air by combined means of elemental analysis, Fourier transform IR, differential thermal analysis/thermogravimetry, X-ray diffraction, and Raman spectroscopy. Characterizations of the resultant TiO2 powders were achieved by scanning electron microscopy, high-resolution transmission electron microscopy, the Brunauer-Emmett-Teller analysis, thermal desorption spectroscopy, and UV-vis spectroscopy. Simultaneous doping of C, N, and Cl was realized upon pyrolyzing the molecular precursor in air, leading to significantly lowered direct and indirect interband transition energies of the resultant TiO2. As a consequence, the anatase nanopowders obtained at 450 and 500 degrees C, with specific surface areas of 97.8 and 64.1 m2/g, respectively, exhibit significantly higher efficiency than Degussa P25 in the bleaching of methyl orange solution under visible light (mainly consisting two wavelengths of 405 and 436 nm at 81:100 intensity ratio) irradiation, either at a fixed weight of TiO2 loading or at a fixed surface area of the loaded TiO2 powder.

Comparison of gastropod mollusc (Apogastropoda: Hydrobiidae) habitats in two crater lakes in Nicaragua

The aquatic gastropod mollusc, Pyrgophorus coronatus, may perform an important role in the transmission of an emergent ocular pathology among fishes in Lake Apoyo, Nicaragua. This disease emerged after an introduction of tilapia (Oreochromis niloticus) and the subsequent loss of Chara sp. beds in the lake. We compared the mollusc population densities in three habitats (sandy/muddy substrates, rocks, and Chara vegetation) at varying depths (1.5, 10, 20, and 30 m) in two volcanic crater lakes in Nicaragua: Lake Apoyo and Lake Xiloa. where lower numbers of affected fishes were found and tilapia has not been introduced. Duplicate samples at 1.5 m depth were taken in each habitat monthly for a year, and triplicate samples for bathymetric analysis of snail populations were performed during August, 2005. Samples of fixed surface area were filtered in a 0.4 cm size screen and live snails were counted from each sample. The preferred snail habitat in both lakes, Chara beds, was vastly reduced in Lake Apoyo via consumption by introduced Nile tilapia (Oreochromis niloticus). Structureless sandy substrates (mean +/- standard error 3.1+/-1.3 ind/m2) had lower population densities than other habitats in Lake Xiloa (rocks 590.9+/-185.3 ind/m2; vegetation 3 686.5+/-698.2 ind/m2; ANOVA 1, p<0.01 in both cases) but this difference was attenuated in Lake Apoyo (sand 384.4+/-111.1 ind/m2; rocks 1 480.4+/-384.8 ind/m2: 0.0 1<p<0.05), where the snails on sandy bottoms were mostly embedded in filamentous algae coating this substrate. Snail population densities in Chara were lower at 20 m than more shallow depths in both lakes. Chara was not found at 1.5 m depth in Lake Apoyo, and was not present at 30 m depth in either lake. Shell lengths in rocky substrate in Lake Apoyo (3.62+/-0.12 mm) were greater than in Lake Xiloá (2.39+/-0.12 mm), suggesting differential snail predation levels in the lakes (p<0.005). Snail populations increased by 67 % inside exclusion cages in sandy substrates in Lake Apoyo (paired t-test, p<0.05), demonstrating the importance of foraging pressure on snail populations. Snail populations in open cages, on the other hand, were reduced by 23 % (p<0.05), suggesting the importance of subacuatic structure in feeding areas for molluscivorous fishes. We found a significant preference toward Chara by the snails (p<0.05) and significant foraging pressure on them (p<0.05) in sandy/muddy substrates. The disruption of Chara by introduced tilapias in Lake Apoyo may play a role in the emergence of ocular pathologies in the lake.

Filiform Corrosion on 6000 Series Aluminium: Kinetics and Inhibition Strategies

High levels of surface shear experienced during rolling, grinding or machining can cause 6000 series aluminium to develop an ultra-fine grained surface layers which dramatically increase susceptibility to filiform corrosion (FFC) under paint films. In-situ Scanning Kelvin Probe (SKP) measurements in humid air are used to compare the kinetics and mechanism of FFC on abraded and lacquer-coated samples of high copper containing AA6111 and low level copper AA6016. FFC is initiated by applying a small volume of aqueous HCl to a penetrative defect on polyvinylbutyral (PVB) coated alloy samples prior to placement in a chamber maintained at constant humidity and temperature. The SKP is then repeatedly scanned over a fixed surface area to produce a time-lapse animation showing the dynamic evolution of localized free corrosion potential patterns. The spatial distribution of potential variation provides insight into the FFC mechanism and the numerical integration of areas of dissimilar potential provides a measure of the time-dependent area of coating delamination. Various possible FFC inhibition strategies are investigated for use under circumstances where removal of the surface layer prior to application of an organic (paint) coating is not feasible. The two strategies shown in this paper are the use of an anti-corrosion pigments based on an intrinsically conducting polymer called polyaniline. An anion-exchange pigment called hydrotalcite is also used.

Development of a Micro Swimming Robot Using Optimised Giant Magnetostrictive Thin Films

A fish-like swimming micro robot is developed using an optimised fin actuator made of giant magnetostrictive films (GMFs). The force oscillation dynamic model of a GMF cantilever with variable cross-section area is derived, and the propulsive model of the fish robot in liquid is established. A discrete variate method for optimising caudal fin configuration is proposed to optimise its propulsive force and drive efficiency under the constraints of fixed surface area and sufficient fin end strength. Both theoretical analysis and experimental results have confirmed that the optimised caudal fin configuration can generate more powerful propulsion and improved efficiency.

Reducing Absorbed Dose by Optimizing Chip Dimensions

The radiation susceptibilities of VLSI chips to x- and gamma-ray photons of energy ranging from 0.06 to 10 MeV are calculated. Chips of different dimensions and fixed surface area are considered.

Morphology of Axisymmetric Vesicles with Encapsulated Filaments and Impurities

The shape deformation of a three-dimensional axisymmetric vesicle with encapsulated filaments or impurities is analyzed by integrating a dissipative dynamics. This method can incorporate systematically the constraint of a fixed surface area and/or a fixed volume. The filament encapsulated in a vesicle is assumed to take a form of a rod or a ring so as to imitate cytoskeletons. In both cases, results of the shape transition of the vesicle are summarized in phase diagrams in the phase space of the vesicular volume and a rod length or a ring radius. We also study the dynamics of a vesicle with impurities coupled to the membrane curvature. The phase separation and the associated shape deformation in the early stage of the dynamical evolution can well be explained by the linear stability analysis. Long runs of simulation demonstrate the nonlinear coarsening of the wavy deformation of the vesicle in the late stage.

Computer Simulations of Surfactant Mixtures at the Liquid/Liquid Interface

We performed molecular dynamics simulations on monolayers of surfactant mixtures at the water/carbon tetrachloride interface. The mixture was composed of sodium dodecyl sulfate (SDS) anionic surfactants and molecules that were chosen to be identical to SDS except that the charges were different in order to make them nonionic. Simulations were conducted for different concentrations of the monolayer mixture; i.e., at a fixed surface area we kept the number of SDS molecules constant while the number of the nonionic molecules was increased. Simulations of different SDS/nonionic mixtures show that the location of the surfactants in the interface is determined by the interaction and the charge distribution of the molecules. We also observe that the structure of the two different surfactants in the monolayer is different and is affected by the concentration of the mixture. For a particular SDS/nonionic mixture, the results indicate that the tails of the SDS molecules are less ordered than the tails of the nonion...