Annular Membrane Research Articles

COMPUTER ASSISTED PROOF OF SPURIOUS EIGENSOLUTION FOR ANNULAR AND ECCENTRIC MEMBRANES

Spurious eigensolutions in the boundary integral equation (BIE) or boundary e1ement method (BEM) for doub1yconnected domain problems, the eccentric and annular membranes, are studied analytically and numerically in this paper. For the mathematica1 ana1ysis, we employ the null-field integral equation, the degenerate kernels and the Fourier series to prove the existence of spurious eigensolutions in the continuous system. Examples of eccentric case, annular membrane and general shape are solved by using the null-field equation approach and BEM, respectively. Based on the numerical experiment, computer-assisted proof for the existence of spurious eigenvalues in companion with the trivial outer boundary data is given. The spurious eigenvalue is found to be the true eigenvalue of a circular membrane with the inner radius. The SVD structure for the four influence matrices is examined Also, the trivial outer boundary densities are found in case of spurious eigenva1ues and are shown in the bar chart.

Discrete Singular Convolution for Free Vibration Analysis Annular Membranes

In this paper, we investigate the effects of some geometric parameters and density variation on frequency characteristics of the annular membranes with varying density. The discrete singular convolution method based on regularized Shannon’s delta kernel is applied to obtain the frequency parameter. The obtained results have been compared with the analytical and numerical results of other researchers, which showed well agreement.

Free vibration of circular and annular membranes with varying density by the method of discrete singular convolution

A numerical method is developed to investigate the effects of some geometric parameters and density variation on frequency characteristics of the circular and annular membranes with varying density. The discrete singular convolution method based on regularized Shannon's delta kernel is applied to obtain the frequency parameter. The obtained results have been compared with the analytical and numerical results of other researchers, which showed well agreement.

Computational modeling of reconstructive surgery: The effects of the natural tension on skin wrinkling

A computational model is presented for the simulation of procedures of reconstructive surgery characterized by the excision of a cutaneous defect and the closure and suture of the wound edges. The skin is modeled as a plane membrane with zero flexural stiffness. The membrane undergoes large deformations and is characterized by a Fung type constitutive response in biaxial tension. Skin wrinkling, which is a typical outcome of the surgery in the form of extrusion of the wound edges and dog-ears, is considered through a modification of the elastic potential as originally proposed by Pipkin's Relaxed Energy Density theory [A.C. Pipkin, The relaxed energy density for isotropic elastic membranes, IMA J. Appl. Math. 36 (1986) 85–99; A.C. Pipkin, Relaxed energy density for large deformations of membranes, IMA J. Appl. Math. 52 (1994) 197–308]. The post-buckling analysis of a stretched annular membrane performed by Geminard et al. [Wrinkle formations in axi-symmetrically stretched membranes, Eur. Phys. J. E 15 (2004) 117–126] is used to validate the model under conditions similar to those of the surgery and to discuss the influence of a pre-existing tension in the membrane on the extension of the wrinkled regions. The model is applied to simulate different surgical procedures and investigate the effects of the natural state of the skin and the shape and size of the excisions. The results explain and validate current practice.

Symmetrical Solutions for Edge-Loaded Annular Elastic Membranes

The Föppl–Hencky nonlinear membrane theory is employed to study the axisymmetric deformation of annular elastic membranes. The general solutions for displacements and stresses are established for arbitrary edge boundary conditions. New exact solution results are developed for central loading and edge forcing conditions. Both positive and negative radial stress solutions are found. Comparisons are made for special cases to previously known solutions with excellent agreement.

A sector elliptic p-element applied to membrane vibrations

A new sector p-element is derived and implemented in elliptic coordinates. The element is applied to the free vibration analysis of annular elliptic membranes. The internal shape functions are derived from the shifted Legendre orthogonal polynomials. The stiffness and mass matrices may be integrated exactly using symbolic computing. One-quarter of the annular elliptic membrane is modeled as one element. The solution of the whole membrane is obtained from the solution of one-quarter with appropriate boundary conditions along the symmetry lines. The accuracy of the solution is improved simply by increasing the polynomial degree. Values for the natural frequencies of annular elliptic membranes are obtained and compared with published results. Comparisons show good agreement. New highly accurate values for the natural frequencies of annular elliptic membranes with different aspect ratios and boundary conditions are presented. A case of a sector annular elliptic membrane is also shown.

Linearly elastic annular and circular membranes under radial, transverse, and torsional loading. Part I: large unwrinkled axisymmetric deformations

Three theories for determination of the equilibrium states of initially flat, linearly elastic, rotationally symmetric, taut membranes are considered: Foppl-von Karman theory, Reissner’s theory, and a new generalization of Reissner’s theory that does not restrict the strains to be small. Attention is focused on annular membranes, but circular membranes are also treated. Large deformations are allowed, and the equilibrium equations are written in terms of transverse, radial, and circumferential displacements. Problems considered include radial stretching, transverse displacement of the inner edge, an adhesive punch pull-off test on a circular blister, transverse pressure, ponding of annular and circular membranes, a vertical distributed load with a vertically sliding outer membrane edge, pull-in (snap-down, jump-to-contact) instability of a MEMS device, torsion of the inner or outer edge of a stretched membrane, and a combination of radial stretching, vertical displacement, and torsion. Results for the three theories are compared. Closed-form solutions are available in a few cases, but usually a shooting method is utilized to obtain numerical solutions for displacements, strains, and stresses. Conditions for the onset of wrinkling are determined. In the second part of this two-part study, small vibrations about equilibrium configurations are analyzed.

Linearly elastic annular and circular membranes under radial, transverse, and torsional loading. Part II: Vibrations about deformed equilibria

Equilibrium configurations of annular and circular membranes involving large displacements were determined in Part I of this study. Now small vibrations about such equilibrium states are analyzed for annular membranes. The membrane is linearly elastic, initially flat, and taut. Foppl-von Karman theory is used to obtain the linearized vibration equations. The problems considered include inward and outward radial stretching, transverse displacement at the inner edge, transverse pressure, a vertical distributed load with a vertically sliding outer membrane edge, torsion at the inner edge along with outward stretching, and in-plane vibrations for cases having a flat equilibrium shape. In many of the cases the transverse motion is coupled with radial and circumferential motions. A shooting method is used to obtain vibration frequencies and corresponding vibration modes with different numbers of nodal diameters and nodal circles. The effects of Poisson’s ratio, in-plane radial and circumferential inertias, the ratio of the radii of the inner and outer edges, and the loading magnitude on the vibration frequencies are investigated.

Effects of the organophosphorus plant growth regulator melaphen on structural characteristics of animal and plant membranes

Effects of low (from 4 × 10−12 to 2 × 10−7 M) doses of the organophosphorus plant growth regulator Melaphen on structural characteristics of plant and animal cellular membranes were compared with special reference to changes in the microviscosity of free membrane lipid bilayers and annular lipids bound to protein clusters. It was found that effective concentrations of Melaphen were not only different for animal and plant membranes, but also discrete and equal to 2 × 10−7 or 4 × 10−12 M depending on the membrane origin and the nature of membrane lipid components. In parallel experiments, effects of Melaphen on the rate of lipid peroxidation (LPO) in biological membranes were studied under conditions of external cold stress. The intensity of LPO was decreased at all Melaphen concentrations able to modulate the microviscosities of free and annular membrane lipids. It is concluded that effects of low and ultra-low Melaphen concentrations on structural and functional states of biological membranes of plant and animal origin are mediated by its interaction with signaling receptors of cellular membranes and cell organelles of both plant and animal origin.

Development and Features of Hydro-membrane Gas Chromatography

Hydro-membrane gas chromatography (HMGC) is achieved by the annular condensation of water in a capillary column at less than 70 degrees C. The annular membrane of water is formed as a result of the wettability of the stationary phase, which is induced at a water contact angle ranging from 75 degrees to 79 degrees, as derived from a solubility parameter (delta) range of 15.7 +/- 0.3 MPa(1/2) of the coated resin. The range of the liquid to gas volume ratio (beta) required to support the annular membrane should be kept between 0.00005 and 0.0003. In the case of a 0.25-mm i.d. column, the ratio can be set by the combination of a 0.1 to 0.2 microl min(-1) water supply rate and helium gas flow rate. Separation by HMGC develops not only a gas-solid partition but also a focusing effect on the water membrane. One feature of HMGC is that it gives a non-adsorption chromatogram based on the blocking effect of pre-adsorbed water; furthermore, despite the presence of a relatively large quantity of water, the electron impact ionization efficiency is kept the same as in the usual GC/MS condition. The detection limit with the injection of 1 microl of aquatic solution was estimated to be less than 0.1 ppb of low-molecular-weight fatty acids with s/n = 5 on a mass chromatogram at m/z 45. The HMGC/EI-MS system can be applied to the trace analysis of C1 to C3 volatile acids, volatile inorganic acids, and halogenated organic acids in water.

Stirred Cell Membrane Emulsification and Factors Influencing Dispersion Drop Size and Uniformity

Water-in-oil (w/o) and oil-in-water (o/w) emulsions were generated using 30-μm pore diameter surface membranes to investigate the factors influencing drop size, and the degree of uniformity of drop size distribution, using a stirred cell employing a simple paddle mounted above a circular disc membrane. The importance of the transitional radius, which is the radius at which the vortex around the unbaffled paddle stirrer changes from a forced vortex to a free vortex and the shear stress at the membrane surface below the stirrer is at its greatest, is demonstrated. Monosized emulsions were produced, with drop size distribution coefficient of variation values of 10% for o/w emulsions and 13.5% for w/o emulsions. These tests demonstrated that a membrane of reduced annular operating area (ringed membrane) produced a more monosized o/w emulsion than a membrane where the full area was used to generate the emulsion, without affecting the mean drop size. The improved size distribution was achieved while the transitional radius was located within the ringed annular section of the membrane. The force balance model, applied to drops formed at the surface of the membrane during emulsification, predicted the droplet diameter provided further drop break up within the stirred cell did not occur. Drop break up occurred at Reynolds numbers below 300 for both oil-in-water and water-in-oil dispersions. Therefore, for Reynolds numbers greater than this, an annular radial ring membrane can be designed to produce monosized droplets using the stirred cell at known continuous phase viscosities with predictable mean droplet size. This knowledge can be used as a design tool to produce monosized droplets of a specified size for various applications using simple stirred cell emulsification.

Generation of curvilinear coordinates on multiply connected regions with boundary singularities

A new algorithm to generate smooth two-dimensional boundary conforming coordinates, with grid lines control, on multiply connected regions including boundary singularities, is devised. The technique fits into the category of elliptic grid generators, since it is based on the numerical solution of Poisson equations. The physical domain D is transformed into a topologically equivalent connected rectangular domain D ′ by defining a branch cut inside D . Control of the grid line spacing over the multiply connected regions is established by appropriately distributing nodal points on the branch cut, and on other boundary curves. Simple and computationally convenient expressions for the control functions, present in the Poisson system, are obtained from this initial distribution of points. Thus, a natural link between clustering properties and the control functions is created. Fixing the nodal points on the branch cut causes the convergence of the numerical method about the singular boundary points. An iterative smoothing process relocating the branch cut is described. As a result, smooth grids are obtained. Grid quality analysis shows that coordinate line orthogonality in the new meshes is superior than in similar grids obtained from a well-known commercial software. The algorithm is successfully tested over a variety of multiply connected domains. The computational advantage of this novel grids is revealed by using them to numerically model the vibrations of complexly shaped annular membranes.

On the applicability of tension field theory to a wrinkling instability problem

The wrinkling instability of a pre-stressed annular membrane loaded uniformly along its inner boundary is investigated with the help of a tension field theory. The theoretical solution is shown to capture the essential qualitative features involved in axisymmetric wrinkling, but displays several limitations regarding the quantitative aspects of this issue. The relationship with some related experimental work reported recently in the literature is also discussed.

Radially isospectral annular membranes

By utilizing transformations of both the radial coordinate and the radial wave function, densities of annular membranes which are radially isospectral to any given radial density are produced. In particular, new families of annular membrane densities are found which are radially isospectral to a uniform membrane. Some new generalizations for completely isospectral annular membranes (including angle-dependent densities) are also given.

Materially-isospectral congruent membranes

Materially-isospectral congruent membranes are membranes which have the same shape but different structure, that is different densities, yet they possess the same vibration frequency spectrum. Some approaches to finding such systems are described, and explicit formulae are presented for some annular and circular membranes. The results are numerically verified.

Changes in cerebral membrane lipid composition and fluidity during thioacetamide‐induced hepatic encephalopathy

Lipids are an essential structural and functional component of cellular membranes. Changes in membrane lipid composition are known to affect the activities of many membrane-associated enzymes, endocytosis, exocytosis, membrane fusion and neurotransmitter uptake, and have been implicated in the pathophysiology of many neurodegenerative disorders. In the present study, we investigated changes in the lipid composition of membranes isolated from the cerebral cortex of rats treated with thioacetamide (TAA), a hepatotoxin that induces fulminant hepatic failure (FHF) and thereon hepatic encephalopathy (HE). HE refers to acute neuropsychiatric changes accompanying FHF. The estimation of membrane phospholipids, cholesterol and fatty acid content in cerebral cortex membranes from TAA-treated rats revealed a decrease in cholesterol, phosphatidylserine, sphingomyelin, a monounsaturated fatty acid, namely oleic acid, and the polyunsaturated fatty acids gamma-linolenic acid, decosa hexanoic acid and arachidonic acid compared with controls. Assessment of membrane fluidity with pyrene, 1,6-diphenyl-1,3,5-hexatriene and 1-[4-(trimethylammonio)phenyl]-6-phenyl-1,3,5-hexatriene revealed a decrease in the annular membrane fluidity, whereas the global fluidity was unaffected. The level of the thiobarbituric acid reactive species marker for lipid peroxidation also increased in membranes from TAA-treated rats, thereby indicating the prevalence of oxidative stress. Results from the present study demonstrate gross alterations in cerebral cortical membrane lipid composition and fluidity during TAA-induced HE, and their possible implications in the pathogenesis of this condition are also discussed.

Compound heterozygosity for mutations in LMNA causes a progeria syndrome without prelamin A accumulation

LMNA-associated progeroid syndromes have been reported with both recessive and dominant inheritance. We report a 2-year-old boy with an apparently typical Hutchinson-Gilford progeria syndrome (HGPS) due to compound heterozygous missense mutations (p.T528M and p.M540T) in LMNA. Both mutations affect a conserved region within the C-terminal globular domain of A-type lamins, defining a progeria hot spot. The nuclei of the patient showed no prelamin A accumulation. In general, the nuclear phenotype did not correspond to that previously described for HGPS. Instead, honeycomb figures predominated and nuclear blebs with reduced/absent expression of B-type lamins could be detected. The healthy heterozygous parents showed similar nuclear changes, although in a smaller percentage of nuclei. Treatment with a farnesylation inhibitor resulted in accumulation of prelamin A at the nuclear periphery, in annular nuclear membrane plaques and in intra/trans-nuclear membrane invaginations. In conclusion, these findings suggest a critical role for the C-terminal globular lamin A/C region in nuclear structure and support a major contribution of abnormal assembly to the progeroid phenotype. In contrast to earlier suggestions, we show that prelamin A accumulation is not the major determinant of the progeroid phenotype.

Evaluation of a Pumping Assist Lung That Uses a Rotating Fiber Bundle

A paracorporeal respiratory assist lung (PRAL) is being developed for supplemental gas exchange to allow the native lungs of acute lung failure patients to heal. The device consists of a rotating annular microporous hollow fiber membrane bundle. The rotation augments the gas exchange efficiency of the device at constant flow-rate thereby uncoupling gas exchange and flow rate. The rotating fibers also enable the PRAL to pump the blood without the need for an additional pump or arterial cannulation. Blood flow rates will be between 500 and 750 ml/min with CO(2) removal rates of 100-130 ml/min. A prototype was manufactured with an overall surface area of 0.25 m. When rotated at 1500 rpm, CO(2) removal increased by 133% and O(2) transfer increased by 157% during an in vitro bovine blood study. The pumping of the rotating fiber bundle was assessed in a glycerol/water solution. At 1500 rpm, the PRAL generated 750 ml/min against 52 mm Hg pressure. Hemolysis of the device was assessed using in vitro bovine blood from a slaughterhouse. Plasma free hemoglobin levels were similar regardless of whether the rotating fibers were present in the PRAL, indicating that a rotating fiber bundle can be used to increase gas exchange without causing blood trauma.

Controlling growth and field emission properties of silicon nanotube arrays by multistep template replication and chemical vapor deposition

A multistep template replication route was employed to fabricate highly ordered silicon nanotube (SiNT) arrays, in which annular nanochannel membranes were produced first, and then silicon was deposited into the annular nanochannels by pyrolytic decomposition of silane. Electron microscopy revealed that these SiNTs are highly crystalline and the wall thicknesses can be controlled by the spaces of the annular nanochannel. Field emission characterization showed that the turn-on field and threshold field for the SiNT arrays are about 5.1V∕μm and 7.3V∕μm, respectively. These results represent one of the lowest fields ever reported for Si field emission materials at technologically useful current densities.

Analytical and experimental investigation on a vibrating annular membrane attached to a central free, rigid core

The natural frequencies of a membrane-central core system are computed and compared with the experimental data from a modified capacitive microphone excited by an electrostatic actuator in a vacuum chamber under controlled temperature conditions. The observed frequencies confirm those from the theoretical model to within ≲ 2 % .