Asymptotic analysis of thin plates under normal load and horizontal edge thrust

We consider the radially symmetric nonlinear von Kármán plate equations for circular or annular plates in the limit of small thickness. The loads on the plate consist of a radially symmetric pressure load and a uniform edge load. The dependence of the steady states on the edge load and thickness is studied using asymptotics as well as numerical calculations. The von Kármán plate equations are a singular perturbation of the Fӧppl membrane equation in the asymptotic limit of small thickness. We study the role of compressive membrane solutions in the small thickness asymptotic behavior of the plate solutions.

We give evidence for the existence of a singular compressive solution for the circular membrane and show by a singular perturbation expansion that the nonsingular compressive solution approach this singular solution as the radial stress at the center of the plate vanishes. In this limit, an infinite number of folds occur with respect to the edge load. Similar behavior is observed for the annular membrane with zero edge load at the inner radius in the limit as the circumferential stress vanishes.

We develop multiscale expansions, which are asymptotic to members of this family for plates with edges that are elastically supported against rotation. At some thicknesses this approximation breaks down and a boundary layer appears at the center of the plate. In the limit of small normal load, the points of breakdown approach the bifurcation points corresponding to buckling of the nondeflected state. A uniform asymptotic expansion for small thickness combining the boundary layer with a multiscale approximation of the outer solution is developed for this case. These approximations complement the well known boundary layer expansions based on tensile membrane solutions in describing the bending and stretching of thin plates. The approximation becomes inconsistent as the clamped state is approached by increasing the resistance against rotation at the edge. We prove that such an expansion for the clamped circular plate cannot exist unless the pressure load is self-equilibrating.

An experimental investigation of the heat transfer from a buoyant gas plume to a horizontal unobstructed ceiling

This thesis presents an experimental investigation of the axisymmetric heat transfer from a small scale fire and resulting buoyant plume to a horizontal, unobstructed ceiling during the initial stages of development. A propane-air burner yielding a heat source strength between 1.0 kW and 1.6 kW was used to simulate the fire, and measurements proved that this heat source did satisfactorily represent a source of buoyancy only. The ceiling consisted of a 1/16" steel plate of 0.91 m. diameter, insulated on the upper side. The ceiling height was adjustable between 0.5 m and 0.91 m. Temperature measurements were carried out in the plume, ceiling jet, and on the ceiling.

Heat transfer data were obtained by using the transient method and applying corrections for the radial conduction along the ceiling and losses through the insulation material. The ceiling heat transfer coefficient was based on the adiabatic ceiling jet temperature (recovery temperature) reached after a long time. A parameter involving the source strength Q and ceiling height H was found to correlate measurements of this temperature and its radial variation. A similar parameter for estimating the ceiling heat transfer coefficient was confirmed by the experimental results.

This investigation therefore provides reasonable estimates for the heat transfer from a buoyant gas plume to a ceiling in the axisymmetric case, for the stagnation region where such heat transfer is a maximum and for the ceiling jet region (r/H ≤ 0.7). A comparison with data from experiments which involved larger heat sources indicates that the predicted scaling of temperatures and heat transfer rates for larger scale fires is adequate.

Seed dormancy and germination of Ficus lundellii and tropical forest restoration

We investigated seed dormancy and germination in Ficus lundellii Standl. (Moraceae), a native species of Mexico's Los Tuxtlas tropical rain forest. In an 8-h photoperiod at an alternating diurnal (16/8 h) temperature of 20/30 degrees C, germination was essentially complete (96%) within 28 days, whereas in darkness, all seeds remained dormant. Neither potassium nitrate (0.05-0.2%) applied continuously nor gibberellic acid applied either continuously (10-200 ppm) or as a 24 hour pretreatment (2000 ppm) induced germination in the dark. Germination in the light was not reduced by a 24-h hydrochloric acid (0.1-1%) pretreatment, but it was reduced both by a 24-h pretreatment with either H2O2 (0. 1-5 M) or 5% HCl, or by more than 5 days of storage at 40 degrees C (4.5% seed water content). In a study with a 2-dimensional temperature gradient plate, seeds germinated fully and rapidly in the light at a constant temperature of 30 degrees C, and fully but less rapidly in the light at alternating temperatures with low amplitudes (< 12 degrees C) about the optimal constant temperature. The base, optimal and ceiling temperatures for rate of germination were estimated as 13.8, 30.1 and 41.1 degrees C, respectively. In all temperature regimes, light was essential for the germination of F lundellii seeds.

Shear strength of composite plate girders with web cutouts

An experimental investigation of the shear strengths of composite plate girders, with centrally placed rectangular web cutouts, is described. A series of tests is conducted on short‐span girders having conventional welded stud shear connectors, connecting the composite concrete slabs to the top flanges of the plate girders. These tests indicated that it is the tensile or pullout capacity of the connectors that is primarily responsible for sustaining the composite action under predominantly shear loading. Subsequently, a further series of tests is conducted on short‐span girders with bolted tension connectors, designed to offer negligible resistance to horizontal shear forces at the interfaces between the concrete slabs and plate girders, which confirmed the previous conclusion. Both series of tests indicate that if adequate connectors are provided between a plate girder and a composite concrete slab, the shear strength of the composite girder is significantly higher than that of the plate girder alone. A simple analytical model for predicting the shear strengths of composite plate girders is also presented, which shows satisfactory correlation with the test results.

Influence on alveolar resorption of the buccal bony plate width in the edentulous ridge expansion (ERE) - an experimental study in the dog

Objective: To compare the hard tissue changes at implants installed applying edentulous ridge expansion (E.R.E.) at sites with a buccal bony wall thickness of 1 or 2 mm.Material and methods: In six Labrador dogs, the first and second maxillary incisors were extracted, and the buccal alveolar bony plates and septa were removed. After 3 months of healing, partial-thickness flaps were dissected, and the E.R.E. was applied bilaterally. Hence, an expansion of the buccal bony crest was obtained in both sides of the maxilla with a displacement of either a 1- or a 2-mm-wide buccal bony plate at the test and control sites, respectively. After 3 months of healing, biopsies were obtained for histological analyses.Results: A buccal vertical resorption of the alveolar crest of 2.3 +/- 0.8 and 2.1 +/- 1.1 mm, and a coronal level of osseointegration at the buccal aspect of 2.7 +/- 0.5 and 2.9 +/- 0.9 mm were found at the test (1 mm) and control (2 mm) sites, respectively. The differences did not reach statistical significance. The mean values of the mineralized bone-to-implant contact (MBIC%) ranged from 62% to 73% at the buccal and lingual sites. No statistically significant differences were found. Horizontal volume gains of 1.8 and 1.1 mm were observed at the test and control sites, respectively, and the difference being statistically significant.Conclusions: Implants installed using the E.R.E. technique yielded a high degree of osseointegration. It is suggested that the displacement of buccal bony plates of 1 mm thickness is preferable compared with that of wider dimensions.

optomotor-blind and the horizontal and vertical system cells of the drosophila optic lobes

The horizontal and vertical system neurons (HS and VS cells) are part of a conserved set of lobula plate giant neurons (LPGNs) in the optic lobes of the adult brain. Structure and physiology of these cells are well known, predominantly from studies in larger Dipteran flies. Our knowledge about the ontogeny of these cells is limited and stems predominantly from laser ablation studies in larvae of the house fly Musca domestica. These studies suggested that the HS and VS cells stem from a single precursor, which, at least in Musca, has not yet divided in the second larval instar. A regulatory mutation (In(1)omb[H31]) in the Drosophila gene optomotor-blind (omb) leads to the selective loss of the adult HS and VS cells. This mutation causes a transient reduction in omb expression in what appears to be the entire optic lobe anlage (OLA) late in embryogenesis. Here, I have reinitiated the laser approach with the goal of identifying the presumptive embryonic HS/VS precursor cell in Drosophila. The usefulness of the laser ablation approach which has not been applied, so far, to cells lying deep within the Drosophila embryo, was first tested on two well defined embryonic sensory structures, the olfactory antenno-maxillary complex (AMC) and the light-sensitive Bolwing´s organ (BO). In the case of the AMC, the efficiency of the ablation procedure was demonstrated with a behavioral assay. When both AMCs were ablated, the response to an attractive odour (n-butanol) was clearly reduced. Interestingly, the larvae were not completely unresponsive but had a delayed response kinetics, indicating the existence of a second odour system. BO will be a useful test system for the selectivity of laser ablation when used at higher spatial resolution. An omb-Gal4 enhancer trap line was used to visualize the embryonic OLA by GFP fluorescence. This fluorescence allowed to guide the laser beam to the relevant structure within the embryo. The success of the ablations was monitored in the adult brain via the enhancer trap insertion A122 which selectively visualizes the HS and VS cell bodies. Due to their tight clustering, individual cells could not be identified in the embryonic OLA by conventional fluorescence microscopy. Nonetheless, systematic ablation of subdomains of the OLA allowed to localize the presumptive HS/VS precursor to a small area within the OLA, encompassing around 10 cells. Future studies at higher resolution should be able to identify the precursor as (an) individual cell(s). Most known lethal omb alleles do not complement the HS/VS phenotype of the In(1)omb[H31] allele. This is the expected behaviour of null alleles. Two lethal omb alleles that had been isolated previously by non-complementation of the omb hypomorphic allele bifid, have been reported, however, to complement In(1)omb[H31]. This report was based on low resolution paraffin histology of adult heads. Four mutations from this mutagenesis were characterized here in more detail (l(1)omb[11], l(1)omb[12], l(1)omb[13], and l(1)omb[15]). Using A122 as marker for the adult HS and VS cells, I could show, that only l(1)omb[11] can partly complement the HS/VS cell phenotype of In(1)omb[H31]. In order to identify the molecular lesions in these mutants, the exons and exon/intron junctions were sequenced in PCR-amplified material from heterozygous flies. Only in two mutants could the molecular cause for loss of omb function be identified: in l(1)omb[13]), a missense mutation causes the exchange of a highly conserved residue within the DNA-binding T-domain; in l(1)omb[15]), a nonsense mutation causes a C-terminal truncation. In the other two mutants apparently regulatory regions or not yet identified alternative exons are affected. To see whether mutant OMB protein in the missense mutant l(1)omb[13] is affected in DNA binding, electrophoretic shift assays on wildtype and mutant T-domains were performed. They revealed that the mutant no longer is able to bind the consensus palindromic T-box element.

Length of the annular regime for condensing flows inside a horizontal channel - the experimental determination of its values and its trends

The experiments observe and measure the length of the annular regime in fully condensing quasi-steady (steady-in-the-mean) flows of pure FC-72 vapor in a horizontal condenser (rectangular cross-section of 2 mm height, 15 mm width, and 1 m length). The sides and top of the duct are made of clear plastic that allows flow visualization. The experimental system in which this condenser is used is able to control and achieve different quasi-steady mass flow rates, inlet pressures, and wall cooling conditions (by adjustment of the temperature and flow rate of the cooling water flowing underneath the condensing-plate). The reported correlations and measurements for the annular length are also vital information for determining the length of the annular regime and proposing extended correlation (covering many vapors and a larger parameter set than the experimentally reported version here) by ongoing independent modeling and computational simulation approach.

Three-Dimensional Mechanics of Yakutat Convergence in the Southern Alaskan Plate Corner

Three-dimensional numerical models are used to investigate the mechanical evolution of the southern Alaskan plate corner where the Yakutat and the Pacific plates converge on the North American plate. The evolving model plate boundary consists of Convergent, Lateral, and Subduction subboundaries with flow separation of incoming material into upward or downward trajectories forming dual, nonlinear advective thermal/mechanical anomalies that fix the position of major subaerial mountain belts. The model convergent subboundary evolves into two teleconnected orogens: Inlet and Outlet orogens form at locations that correspond with the St. Elias and the Central Alaska Range, respectively, linked to the East by the Lateral boundary. Basins form parallel to the orogens in response to the downward component of velocity associated with subduction. Strain along the Lateral subboundary varies as a function of orogen rheology and magnitude and distribution of erosion. Strain-dependent shear resistance of the plate boundary associated with the shallow subduction zone controls the position of the Inlet orogen. The linkages among these plate boundaries display maximum shear strain rates in the horizontal and vertical planes where the Lateral subboundary joins the Inlet and Outlet orogens. The location of the strain maxima shifts with time as the separation of the Inlet and Outlet orogens increases. The spatiotemporal predictions of the model are consistent with observed exhumation histories deduced from thermochronology, as well as stratigraphic studies of synorogenic deposits. In addition, the complex structural evolution of the St Elias region is broadly consistent with the predicted strain field evolution. Citation: Koons, P. O., B. P. Hooks, T. Pavlis, P. Upton, and A. D. Barker (2010), Three-dimensional mechanics of Yakutat convergence in the southern Alaskan plate corner, Tectonics, 29, TC4008, doi: 10.1029/2009TC002463.

Wedges and plate-bandes: mechanical theories after De la Hire

Plate-bandes are straight masonry arches (they are called, also, flat arches or lintel arches). Ideally they have the surfaces of extrados and intrados plane and horizontal. The stones or bricks have radial joints converging usually in one centre. The voussoirs have the form of wedges and in French they are called "claveaux". A plate-bande is, in fact, a lintel made of several stones and the proportions of lintels and plate-bandes are similar. Proportions of plate-bandes, that is the relationship between the thickness t and the span s (t/s)varies, typically between 1/4–1/3 in thick plate-bandes, and is less than 1/20 in the most slender ones. A ratio of circa 1/8 was usual in the 18th Century and follows a simple geometrical rule: the centre form with the intrados an equilateral triangle and the plate-bande should contain an arc of circle. The joints are usually plane, but in some cases present a «rebated» or «stepped» form. Plate-bandes exert an inclined thrust as any masonry arch. This thrust is usually very high and it requires either massive buttresses, or to be built in the middle of thick walls. Master builders and architects have tried since antiquity to calculate the abutment necessary for any arch. A modern architect or engineer will measure the arch thrust in units of force, kN or tons. Traditionally, the thrust has been measured as the size of the buttresses to resist it safely. Old structural rules, then, addressed the design problem establishing a relationship between the span and the depth of the buttress. These were empirical rules, particular for every type of arch or structure in every epoch. Thus, the typical gothic buttress is 1/4 of the vault span, but a Renaissance or baroque barrel vault will need more than 1/3 of the span. A plate-bande would require more than one half of the span; this is precisely the rule cited by the French engineer Gautier, who tried unsuccessfully to justify it by static reasons. They were used, typically, to form the lintels of windows or doors (1-2 m, typically); in Antiquity they were used, also, though rarely, at the gates of city walls or in niches (ca. 2 m, reaching 5.2 m). Plate-bandes may show particular problems: it is not unusual that some sliding of the voussoirs can be observed, particularly in thick plate-bandes. The stepped joints on Fig. 1, left, were used to avoid this problem. There are other «hidden» methods, like iron cramps or the use of stone wedges, etc. In seismic zones these devices were usual. Another problem relates to the deformation; a slight yielding of the abutments, or even the compression of the mortar joints, may lead to some cracking and the descent of the central keystone. Even a tiny descent will convert the original straight line of the intrados in a broken line with a visible «kink» or angle in the middle. Of course, both problems should be avoided. Finally, the wedge form of the voussoirs lead to acute angles in the stones and this can produce partial fractures; this occurs usually at the inferior border of the springers at the abutments. It follows, that to build a successful plate-bande is not an easy matter. Also, the structural study of plate-bandes is far from simple, and mechanics and geometry are related in a particular way. In the present paper we will concentrate on the structural aspects and their constructive consequences, with a historical approach. We will outline the development of structural analysis of plate-bandes from ca. 1700 until today. This brief history has a more than purely academic interest. Different approaches and theories pointed to particular problem, and though the solution given may have been incorrect, the question posed was often pertinent. The paper ends with the application of modern Limit Analysis of Masonry Structures, developed mainly by professor Heyman in the last fifty years. The work aims, also, to give some clues for the actual architect and engineer involved in the analysis or restoration of masonry buildings.

Error, Bias, and Long-Branch Attraction in Data for Two Chloroplast Photosystem Genes in Seed Plants

Sequences of two chloroplast photosystem genes, psaA and psbB, together comprising about 3,500 bp, were obtained for all five major groups of extant seed plants and several outgroups among other vascular plants. Strongly supported, but significantly conflicting, phylogenetic signals were obtained in parsimony analyses from partitions of the data into first and second codon positions versus third positions. In the former, both genes agreed on a monophyletic gymnosperms, with Gnetales closely related to certain conifers. In the latter, Gnetales are inferred to be the sister group of all other seed plants, with gymnosperms paraphyletic. None of the data supported the modern ‘‘anthophyte hypothesis,’’ which places Gnetales as the sister group of flowering plants. A series of simulation studies were undertaken to examine the error rate for parsimony inference. Three kinds of errors were examined: random error, systematic bias (both properties of finite data sets), and statistical inconsistency owing to long-branch attraction (an asymptotic property). Parsimony reconstructions were extremely biased for third-position data for psbB. Regardless of the true underlying tree, a tree in which Gnetales are sister to all other seed plants was likely to be reconstructed for these data. None of the combinations of genes or partitions permits the anthophyte tree to be reconstructed with high probability. Simulations of progressively larger data sets indicate the existence of long-branch attraction (statistical inconsistency) for third-position psbB data if either the anthophyte tree or the gymnosperm tree is correct. This is also true for the anthophyte tree using either psaA third positions or psbB first and second positions. A factor contributing to bias and inconsistency is extremely short branches at the base of the seed plant radiation, coupled with extremely high rates in Gnetales and nonseed plant outgroups. M. J. Sanderson,* M. F. Wojciechowski,*† J.-M. Hu,* T. Sher Khan,* and S. G. Brady

In vivo confocal microscopy of the palpebral conjunctiva and tarsal plate

Purpose The aim of this work is to develop a more complete understanding of the in vivo histology of the human palpebral conjunctiva and tarsal plate. Methods. The upper eyelids of 11 healthy human volunteer subjects were everted, and laser scanning confocal microscopy was used to examine the various tissue layers of the palpebral conjunctiva and tarsal plate. Results The superficial and basal epithelial layers are composed of cells with gray cytoplasm and thick, light gray borders.Nuclei can not be seen. The stroma has a varied appearance; fibrous tissue is sometimes observed, interspersed with dark,amorphous lacunae, and crevases. Numerous single white or gray cells populate this tissue, and fine blood vessels are seen traversing the field. Occasional conjunctival microcysts and Langerhans cells are observed. The tarsal plate is dark and amorphous, and meibomian gland acini with convoluted borders are clearly observed. Acini are composed of an outer lining of large cuboidal cells, and differentiated secretory cells can be seen within the acini lumen. Conclusions Laser scanning confocal microscopy is capable of studying the human palpebral conjunctiva, tarsal plate, and acini of meibomian glands in vivo. The observations presented here may provide useful supplementary anatomical information relating to the morphology of this tissue.