Shallow Curvature Research Articles

Nonlinear analysis of thermal–mechanical bending of laminated composite shallow arches reinforced with GPLs

The current research presents an analysis on the nonlinear thermal and mechanical bending problems of nanocomposite arches reinforced by graphene platelets. The graphene nanofillers are distributed through the thickness of the composite arch as the uniform or functionally graded patterns. Thermo-mechanical properties of the nanocomposite arch are evaluated using the Halpin–Tsai rule of mixtures approach. The multi-layered thick arch with shallow curvature is assumed to rest on an elastic nonlinear medium. Equilibrium equations of the assumed arch are obtained using the principle of virtual work and considering the third-order shear deformation theory with the von Kármán type of nonlinearity. The nonlinear governing equations are solved for the nanocomposite arch with immovable simply-supported and clamped–clamped boundaries by using a perturbation-based technique. Different numerical results are presented in this paper to evaluate the effects of curvature ratio, slenderness ratio, elastic medium, and the weight fraction and distribution pattern of GPLs on the thermal and mechanical bending behaviors of composite arches.

A Simplex Multi-Phase Approach for Modelling Debris Flows in Smoothed-Terrain-Following Coordinate System

Herewith we present a multi-phase model for debris flows, of which the flow body is supposed to be composed of water, fine sediment (clay/silt) and grains. The rheology of debris flows varies due to the dynamical variation of the composition concentrations. In the present study the component of silt/clay is an individual phase, and its concentration plays a key role in determining the rheology of the interstitial fluid. Hence, there are three phases in the mixture, the grain phase, the clay phase and the water phase from the viewpoint of mass conservation. Only the grain phase and fluid phase are considered in the momentum conservation, since the clay is suspended in the fluid and the relative motion is negligible within the interstitial fluid. The grain constituent is treated as a frictional Coulomb-like continuum, and the viscosity of the interstitial depends on the clay concentration. The resultant models are given in a smoothed-terrain-following coordinate system, a compromise between the constraint of shallow curvature for the terrain-fitting coordinate system and retaining the high resolution of the topography. The numerical implementation is developed with the CUDA-library for GPU-high-performance computations. The feasibility and applicability will be presented by back calculation of a historical event.

Nanofiber curvature with Rho GTPase activity increases mouse embryonic fibroblast random migration velocity.

Mechanotransduction arises from information encoded in the shape of materials such as curvature. It induces activation of small GTPase signaling affecting cell phenotypes including differentiation. We carried out a set of preliminary experiments to test the hypothesis that curvature (1/radius) would also affect cell motility due to signal pathway crosstalk. High molecular weight poly (methyl methacrylate) straight nanofibers were electrospun with curvature ranging from 41 to 1μm-1 and collected on a passivated glass substrate. The fiber curvature increased mouse mesenchymal stem cell aspect ratio (P < 0.02) and decreased cell area (P < 0.01). Despite little effect on some motility patterns such as polarity and persistence, we found selected fiber curvatures can increase normalized random fibroblastic mouse embryonic cell (MEF) migration velocity close to 2.5 times compared with a flat surface (P < 0.001). A maximum in the velocity curve occurred near 2.5μm-1 and may vary with the time since initiation of attachment to the surface (range of 0-20h). In the middle range of fiber curvatures, the relative relationship to curvature was similar regardless of treatment with Rho-kinase inhibitor (Y27632) or cdc42 inhibitor (ML141), although it was decreased on most curvatures (P < 0.05). However, below a critical curvature threshold MEFs may not be able to distinguish shallow curvature from a flat surface, while still being affected by contact guidance. The preliminary data in this manuscript suggested the large low curvature fibers were interpreted in a manner similar to a non-curved surface. Thus, curvature is a biomaterial construct design parameter that should be considered when specific biological responses are desired. Statement of integration, innovation, and insight Replacement of damaged or diseased tissues that cannot otherwise regenerate is transforming modern medicine. However, the extent to which we can rationally design materials to affect cellular outcomes remains low. Knowing the effect of material stiffness and diameter on stem cell differentiation, we investigated cell migration and signaling on fibrous scaffolds. By investigating diameters across orders of magnitude (50-2000nm), we identified a velocity maximum of ~800nm. Furthermore, the results suggest large fibers may not be interpreted by single cells as a curved surface. This work presents insight into the design of constructs for engineering tissues.

Free vibration and snap-through instability of FG-CNTRC shallow arches supported on nonlinear elastic foundation

This paper analytically investigates the nonlinear free vibration and snap-through instability of nanocomposite shallow arches reinforced with carbon nanotubes (CNTs). The functionally graded (FG) carbon nanotube reinforced composite (CNTRC) arch with shallow curvature is analysed under uniformly distributed transverse loading. The arch is assumed to rest on a three-parameter nonlinear elastic foundation in a uniform temperature field. Thermo-mechanical properties of the arch are graded through the thickness and are considered to be temperature-dependent. The equations of motion are established based on a general high-order shear deformation theory. These nonlinear equations are derived by Hamilton’s principle within the framework of the von Kármán assumption. The static equilibrium equations and dynamic equations of motion are solved analytically for the arch with immovable simply supported edges. The two-step perturbation technique and Galerkin method are implemented to obtain the closed-form solutions. The novel results illustrate the influences of CNT distribution pattern, foundation stiffness and geometrical parameters on the linear/nonlinear frequency and snap-through instability of the arch. It is shown that the minimum value of limit loads/frequencies belongs to the FG-O type of nanocomposite arches and the maximum ones are obtained in FG-X pattern.

Dimension reduction for thin films prestrained by shallow curvature

We are concerned with the dimension reduction analysis for thin three-dimensional elastic films, prestrained via Riemannian metrics with weak curvatures. For the prestrain inducing the incompatible version of the Föppl–von Kármán equations, we find the Γ -limits of the rescaled energies, identify the optimal energy scaling laws, and display the equivalent conditions for optimality in terms of both the prestrain components and the curvatures of the related Riemannian metrics. When the stretching-inducing prestrain carries no in-plane modes, we discover similarities with the previously described shallow shell models. In higher prestrain regimes, we prove new energy upper bounds by constructing deformations as the Kirchhoff–Love extensions of the highly perturbative, Hölder-regular solutions to the Monge–Ampere equation obtained by means of convex integration.

On nonlinear vibration and snap-through buckling of long FG porous cylindrical panels using nonlocal strain gradient theory

In the current research, nonlinear vibration and snap-buckling analysis of long cylindrical panels made of functionally graded (FG) porous materials are studied. The case of cylindrical panels with shallow curvature and long length is analyzed using an approximate nonlocal strain gradient model. Non-homogeneous properties of the cylindrical panel with uniform distributed porosities are graded across the thickness. The interaction of the cylindrical panel with a nonlinear elastic foundation is also included into the formulation. The mathematical formulations are expressed based on the high-order shear deformation theory and the Donnell kinematic assumptions. Three nonlinear motion equations of the cylindrical panel are established by employing the Hamilton principle. These coupled partial differential equations are analytically solved for the case of long cylindrical panels which is immovable pinned on both straight edges. The two-step perturbation technique and Galerkin’s method are implemented to extract the nonlinear free vibration and snap-buckling characteristics of the shell. The natural frequencies and load-deflection curves are first validated for the cases of long plates and shells. Afterwards, novel parametric studies are developed to show the effects of nonlocal and length scale parameters, power law index, porosity coefficient, foundation components, and the geometrical parameters of the shell.

On nonlinear vibration and snap-through stability of porous FG curved micro-tubes using two-step perturbation technique

Considering the modified couple stress theory, nonlinear vibration and snap-buckling analyses of porous FG curved micro-tubes are performed in this research. Curved micro-tubes with shallow curvature resting on nonlinear elastic foundation are analysed. Properties of the micro-tube with uniform distributed porosity are graded across the radius of cross-section by means of a power law function. The equations of motion are derived based on the high-order shear deformation theory by applying the Hamilton principle. Governing equations are obtained using the von Kármán assumptions as a system of nonlinear differential equations. For curved micro-tubes which are simply supported in flexure and axially immovable, governing equations are solved using an analytical approach. A two-step perturbation technique is used to obtain the closed-form solutions for nonlinear free vibration and snap-buckling problems. Since the porous FG curved micro-tube is not analysed in literature, the results are compared with the case of FG tubes. Parametric studies are provided to explore the effect of geometrical characteristics of the curved micro-tube on the static and dynamic responses of these structures. The influences of material length scale parameter, functionally graded patterns, porosity parameter and nonlinear elastic foundation are also investigated.

ImageJ SurfCut: a user-friendly pipeline for high-throughput extraction of cell contours from 3D image stacks

BackgroundMany methods have been developed to quantify cell shape in 2D in tissues. For instance, the analysis of epithelial cells in Drosophila embryogenesis or jigsaw puzzle-shaped pavement cells in plant epidermis has led to the development of numerous quantification methods that are applied to 2D images. However, proper extraction of 2D cell contours from 3D confocal stacks for such analysis can be problematic.ResultsWe developed a macro in ImageJ, SurfCut, with the goal to provide a user-friendly pipeline specifically designed to extract epidermal cell contour signals, segment cells in 2D and analyze cell shape. As a reference point, we compared our output to that obtained with MorphoGraphX (MGX). While both methods differ in the approach used to extract the layer of signal, they output comparable results for tissues with shallow curvature, such as pavement cell shape in cotyledon epidermis (as quantified with PaCeQuant). SurfCut was however not appropriate for cell or tissue samples with high curvature, as evidenced by a significant bias in shape and area quantification.ConclusionWe provide a new ImageJ pipeline, SurfCut, that allows the extraction of cell contours from 3D confocal stacks. SurfCut and MGX have complementary advantages: MGX is well suited for curvy samples and more complex analyses, up to computational cell-based modeling on real templates; SurfCut is well suited for rather flat samples, is simple to use, and has the advantage to be easily automated for batch analysis of images in ImageJ. The combination of these two methods thus provides an ideal suite of tools for cell contour extraction in most biological samples, whether 3D precision or high-throughput analysis is the main priority.

Mean-field Matsubara dynamics: Analysis of path-integral curvature effects in rovibrational spectra.

It was shown recently that smooth and continuous "Matsubara" phase-space loops follow a quantum-Boltzmann-conserving classical dynamics when decoupled from non-smooth distributions, which was suggested as the reason that many dynamical observables appear to involve a mixture of classical dynamics and quantum Boltzmann statistics. Here we derive a mean-field version of this "Matsubara dynamics" which sufficiently mitigates its serious phase problem to permit numerical tests on a two-dimensional "champagne-bottle" model of a rotating OH bond. The Matsubara-dynamics rovibrational spectra are found to converge toward close agreement with the exact quantum results at all temperatures tested (200-800 K), the only significant discrepancies being a temperature-independent 22 cm-1 blue-shift in the position of the vibrational peak and a slight broadening in its line shape. These results are compared with centroid molecular dynamics (CMD) to assess the importance of non-centroid fluctuations. Above 250 K, only the lowest-frequency non-centroid modes are needed to correct small CMD red-shifts in the vibrational peak; below 250 K, more non-centroid modes are needed to correct large CMD red-shifts and broadening. The transition between these "shallow curvature" and "deep curvature" regimes happens when imaginary-time Feynman paths become able to lower their actions by cutting through the curved potential surface, giving rise to artificial instantons in CMD.

Diamond micro-lenses with variable height using self-assembly silica-microsphere-monolayer as etching mask

Diamond micro-lenses have potential applications in quantum information processing and high power lasers. Diamond micro-lenses have been fabricated through focused ion beam milling or laser machining followed by mechanical polishing, which are not scalable. Photoresist reflow and plasma etching can fabricate diamond micro-lenses but only with a relatively shallow curvature. In this work, we report the fabrication of diamond micro-lenses with variable height. Silica microspheres with diameters of 2.5 and 3.2μm are dispersed on the diamond surface to form a monolayer as etching mask, following with plasma etching which is used to transfer the spherical shape into diamond substrate. The height of diamond microlens can be tuned by changing the gas mixture ratios. Scanning electron microscope (SEM) has been used to verify the profiles of the micro-lenses. This method is useful for the fabrication of large arrays of diamond micro-lenses for photonic applications.

Evaluation of glutamate concentration transient in the synaptic cleft of the rat calyx of Held

Establishing the spatiotemporal concentration profile of neurotransmitter following synaptic vesicular release is essential for our understanding of inter-neuronal communication. Such profile is a determinant of synaptic strength, short-term plasticity and inter-synaptic crosstalk. Synaptically released glutamate has been suggested to reach a few millimolar in concentration and last for <1 ms. The synaptic cleft is often conceived as a single concentration compartment, whereas a huge gradient likely exists. Modelling studies have attempted to describe this gradient, but two key parameters, the number of glutamate in a vesicle (N(Glu)) and its diffusion coefficient (D(Glu)) in the extracellular space, remained unresolved. To determine this profile, the rat calyx of Held synapse at postnatal day 12-16 was studied where diffusion of glutamate occurs two-dimensionally and where quantification of AMPA receptor distribution on individual postsynaptic specialization on medial nucleus of the trapezoid body principal cells is possible using SDS-digested freeze-fracture replica labelling. To assess the performance of these receptors as glutamate sensors, a kinetic model of the receptors was constructed from outside-out patch recordings. From here, we simulated synaptic responses and compared them with the EPSC recordings. Combinations of N(Glu) and D(Glu) with an optimum of 7000 and 0.3 μm(2) ms(-1) reproduced the data, suggesting slow diffusion. Further simulations showed that a single vesicle does not saturate the synaptic receptors, and that glutamate spillover does not affect the conductance amplitude at this synapse. Using the estimated profile, we also evaluated how the number of multiple vesicle releases at individual active zones affects the amplitude of postsynaptic signals.

Nonlinear Reduced Order Random Response Analysis of Structures with Shallow Curvature

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures with shallow curvature under random loadings. For reduced order analysis, the modal basis selection must be capable of reflecting the coupling in both the linear and nonlinear stiffness. For the symmetric shallow arch under consideration, four categories of modal basis functions are defined. Those having symmetric transverse displacements (ST modes) can be designated as transverse dominated (ST-T) modes and in-plane dominated (ST-I) modes. Those having anti-symmetric transverse displacements (AT modes) can similarly be designated as transverse dominated (AT-T) modes and in-plane dominated (AT-I) modes. The response of an aluminum arch under a uniformly distributed transverse random loading is investigated. Results from nonlinear modal simulations made using various modal bases are compared with those obtained from a numerical simulation in physical degrees-of-freedom. While inclusion of ST-T modes is important for all response regimes, it is found that the ST-I modes become increasingly important in the nonlinear response regime, and that AT-T and AT-I modes are critical in the autoparametric regime.

Visualizing concave and convex partitioning of 2D contours

A new method based on parsing the concavity code is used to partition a digital contour into concave and convex sections. Innovative features of the technique include: (1) coerced two-state classification of every point into a concavity or a convexity; (2) linguistic explanation for each point’s classification; (3) curvature validation via the residue (that portion of the boundary remaining after curvature extraction); (4) preservation of original contour shape; (5) symbolic logic methodology (no floating point operations); (6) parameter-free implementation; (7) linear time and space complexity. No other currently available contour partitioning method exhibits all of these features. The parser achieves two-state partitioning by implementing simple notions of cumulative curvature, vertex adjacency, shallow curvature absorption, and residue sharing. Concavities and convexities are color-coded to help disambiguate complex images such as topographic contour maps and radio frequency propagation plots. To gauge product quality, the observer may appeal visually to the residue for validation.

A boundary concavity code to support dominant point detection

A symbolic algorithm is described to detect dominant points of a simple closed boundary. First, a concavity code is constructed from the Freeman chain code to classify the degree of concavity or convexity of boundary coordinates. Then, dominant points are extracted by discarding shallow curvature sequences of the concavity code, by appealing to a technique called error budgeting.

The vertebral curvature of sportsmen

To characterize the vertebral curvature of individuals from a variety of sporting backgrounds, 380 Japanese males were categorized into 11 groups based on sport participation: rugby, soccer, kendo, swimming, sailing, four track and field events (sprinting, distance running, jumping and throwing), bodybuilding and no athletic engagement. The vertebral curvature of each subject was estimated from a Moire photograph. The vertebral curvature lines of the 11 groups were compared and classified into four types based on the shape of the vertebral curvature: (1) bodybuilders and swimmers; (2) rugby players, sailors, soccer players and non-athletes; (3) kendo participants, middle- and long-distance runners and sprinters; (4) throwers. The relationship between the shape of the vertebral curvature and the characteristics of the sport was determined. We found that posture was specific to the sport. Sprinters, middle- and long-distance runners, jumpers, kendo participants and throwers had a deeply curved vertebral column, whereas swimmers, bodybuilders, sailors, soccer players, rugby players and non-athletes had a shallow curvature.

In-plane vibration of slightly curved laminated composite beams

A complete set of equations for the free and forced vibration analysis of laminated composite beams of shallow curvature is presented. The beam is assumed to be vibrating in its plane. These equations are shown to be consistent by variational derivation. Natural frequencies for simply supported curved beams are obtained by exact solutions. The Ritz method with algebraic polynomials is used to obtain approximate solutions for arbitrary boundary conditions. Natural frequencies for completely free and cantilevered curved beams are presented as examples. Extension-bending coupling due to lamination is distinguished from that due to curvature. Effects of curvature, material orthotropy and lamination sequence on the natural frequencies are studied.

Analysis of the segmentation in the profile of alpine talus slopes

AbstractA method for analysing the segmentation in the profile of talus slopes is used in an Alpine periglacial environment. Two populations of talus slope profiles are examined according to the development of their headwalls. Beneath massive rockwalls the profile appears bi‐segmented: a break point situated at a constant angle (33–34 degrees) divides an extensive proximal segment with a shallow curvature from a shorter and more concave distal segment. When the headwall disappears, the segmentation is modified and a concavity extends throughout the profile. A new model for talus slope formation is proposed in which the rockfall mechanism and the removal processes are combined.

The Current‐Time Relationship during Anodic Oxide Film Growth under High Electric Field

An interpretation of current‐time transients describing anodic oxide film growth on metals is presented. When the rate of oxide film growth is controlled by ion conduction under high electric field, the classical theory of Cabrera and Mott leads to shallow curvature in plots of vs. . Such data can be linearized by using an integrated form of Cabrera and Mott's equation. The predicted form of the current transient shows decaying linearly as from which film growth parameters may be calculated. The equations distinguish sensitively between Cabrera‐Mott film growth kinetics and direct logarithmic film growth kinetics. The effects of the presence of an ohmic potential drop in the electrolyte are shown. The equations are tested in terms of anodic oxide film growth on iron and titanium.

Model studies of oxygen chemisorption on silver surfaces using an AgO2 cluster

Ab initio all electron SCF calculations have been carried out on low lying states of AgO2 of Cs and C 2v symmetry, and on OAgO of D ∞h symmetry, and the results are related to the observed chemisorption properties of dioxygen on silver surfaces. Analytic second derivatives were used to characterize the stationary points on the potential energy surfaces and to obtain harmonic frequencies to compare with the results of electron energy loss spectra. The Cs species are shown to be true minima and a bonding mechanism is proposed which explains the unique stability observed experimentally for the ‘out of plane’ chemisorbed state of dioxygen on Ag(111). Calculations on the C 2v species show these to be transition states for interconversion of the relevant Cs species. While the OAgO species is shown to be unstable, the shallow curvature of the potential energy surface would indicate that on an extended silver surface, dissociation of the dioxygen would be expected, as recently proposed by McKee. The relevance of ...

The tridimensional structure of Nissl bodies: a stereoscopic study in ventral horn cells of rat spinal cord.

The tridimensional structure of rough endoplasmic reticulum was examined with both high and low voltage electron microscopes in large ventral horn cells of rat spinal cord, by combining stereoscopic techniques with the use of thick sections selectively impregnated with heavy metal salts. In all neurons examined Nissl bodies appeared as well defined clusters of densely stained and profusely anastomosed plate-, ribbon-, and thread-like cisternae. Plate-like cisternae were variable in size, often showed a shallow curvature, and usually ran in short parallel arrays, separated from one another by fairly constant intervals. All gave rise at their edges to several ribbon-like extensions which occasionally decreased in width distally, turning into thin, thread-like cisternae. Characteristically, these ribbon-like structures would emerge at an angle from their plate of origin and smoothly curve away from the plane of the plate to merge with ribbons or threads arising from adjacent or more distant plates. Most plate-like cisternae were found at the periphery of Nissl bodies and tended to be oriented parallel to their surface. In contrast, the center of Nissl bodies was almost exclusively occupied by a complex network of ribbon- and thread-like cisternae. It is suggested that the basic plate/ribbon association here described in spinal motoneurons might be a constant feature of Nissl body architecture in various neuronal types, while the size, orientation, and relative proportion of plate-like cisternae may vary according to the metabolic state and/or functional specialization of the cells.