Assembly Of Disks Research Articles

Structure of the amorphous phase in oriented polymers

Changes in the position, width, and shape of the amorphous halo with orientation in the X-ray diffraction patterns of amorphous and semicrystalline polymers are used to study the medium-range order in the amorphous phase. Analysis of the data shows that a fraction of the amorphous domains is preferentially oriented. The chain segments in these domains are more densely packed, and these changes in density are accompanied by changes in the conformation of the polymer chains. The variations in the amorphous scattering are simulated by varying the density of packing of a two-dimensional assembly of hard disks. The diameter of such a disk is ∼4.3 A for polyethylene, which is larger than the Lennard-Jones diameter of 3.9-4.1 A

Arrangement of cells in Voronoi tesselations of monosize packing of discs

Abstract We describe a two-dimensional mosaic obtained by the Voronoi tesselation of a monosize assembly of discs at different packing fractions. The experimental device (hard discs moving on an air table) produces, for every concentration of the discs, a succession of mosaics in statistical equilibrium, which constitutes a statistical ensemble. This ensemble is large enough for fluctuations from the most probable distributions to be negligible. Both topological and metric properties show deviations from those of a totally random mosaic. These deviations can be ascribed to steric exclusions. In particular, distributions of the numbers of sides, of the perimeters and of the areas of the polygons differ from those observed in biological celi assemblies. The Aboav law holds, but with a slope which can be as Iow as 4–66. The Lewis law is obeyed only for smali packing fractions. The variance of the distribution of the number n of polygon sides is a universal function of p 6, the probability of finding a six-si...

Universal properties of Voronoi tessellations of hard discs

The authors describe a 2D mosaic obtained by the Voronoi tessellation of a monosize assembly of discs at different packing fractions. The experimental device (hard discs moving on an air table) produces, for every packing fraction, a succession of mosaics in statistical equilibrium, which constitutes a statistical ensemble. This ensemble is large enough for fluctuations from the most probable distributions to be negligible. They use the maximum entropy principle to get the distribution of the polygons in 2D mosaics generated from an assembly of hard discs. Steric exclusion yields an extra conservation law, which is sufficient to give a good agreement with the experimental data. A similar behaviour in the six-fold parameter seems to hold for other mosaics.

The photoreceptor cytoskeleton and disk turnover

The light sensitive part of the rod photoreceptor, the outer segment, is continually renewed within the retinas of adult vertebrates. This process of membrane renewal consists of two distinct components, disk addition and disk shedding, which are maintained in a constant dynamic balance throughout adult life. Thus, although each rod outer segment loses approximately 10% of its length each day due to shedding and phagocytosis of rod tips by the adjacent pigment epithelial layer, the total length of the outer segment remains constant due to assembly of new disks at the base of the outer segment. The mechanisms of disk shedding and disk addition are, as yet, undefined although it appears that each phase of the overall disk renewal cycle may involve some cytoskeletal components.

Numerical simulations of a compact convergent system of ice floes

The granular nature of the Arctic pack ice, and the plastic nature of the deformation of the pack due to ridging, has long been recognised. However, because of a lack of experimental data, assumptions must be made to define the shape of the yield curve and the associated flow rule which characterize the aggregate rheology of the ice pack. In this work, the results of numerical experiments with a simulated granular viscous-plastic material are presented. The experiments model the granular texture of the ice pack as a dense assembly of non-uniform diameter disks in a rectangular control area. Deformation of the control area is driven by constant strain rates. In the experiments, the ratio of the principal strain rates is varied from isotropic convergence through uniaxial divergence. The stresses computed in the experiments, at the various strain-rate ratios, define a yield curve in principal-stress space. The effects of different coefficients of friction and viscous damping on the shape of the yield curve are explored.

Numerical simulations of a compact convergent system of ice floes

The granular nature of the Arctic pack ice, and the plastic nature of the deformation of the pack due to ridging, has long been recognised. However, because of a lack of experimental data, assumptions must be made to define the shape of the yield curve and the associated flow rule which characterize the aggregate rheology of the ice pack. In this work, the results of numerical experiments with a simulated granular viscous-plastic material are presented. The experiments model the granular texture of the ice pack as a dense assembly of non-uniform diameter disks in a rectangular control area. Deformation of the control area is driven by constant strain rates. In the experiments, the ratio of the principal strain rates is varied from isotropic convergence through uniaxial divergence. The stresses computed in the experiments, at the various strain-rate ratios, define a yield curve in principal-stress space. The effects of different coefficients of friction and viscous damping on the shape of the yield curve are explored.

Constitutive relation for a particulate medium with the effect of particle rotation

The constitutive behavior of granular assemblies is investigated taking into account the effect of particle rotation. Continuum fields are assumed by tensorial polynomial expansion for the discrete variables, namely, particle displacements and rotations. The strain measures for the packing are obtained from the particle displacement and rotation. From the principle of virtual work, the stress measures for the packing are expressed in terms of the contact forces, the contact moments and the geometric measures for the packing structure. The derived stress-strain relationship is then evaluated by an example of a randomly packed assembly of circular disks loaded in two different conditions. Deformation of the packing calculated from the constitutive equations is compared with the results obtained from the discrete method of computer simulation to show the applicability of the method.

Temperature-dependent birefringence patterns in Xenopus rod outer segments

Results reported here show that the birefringence of disk membranes in Xenopus rod photoreceptors depends upon the temperature at which the disks were assembled. Portions of the outer segments produced by the assembly of new disks while frogs are exposed to constant darkness and an ambient temperature of 25 degrees C have a higher birefringence than portions assembled at 18 degrees C. The intensity of birefringence reflects molecular-level structure and macromolecular-level organization of the disk membranes. It has been shown previously that increasing the ambient temperature enhances the rate of assembly of disk membranes in Xenopus rod outer segments. It also has been shown that disk membranes are assembled most frequently in the hours following light onset, and that disks assembled in the light have a lower birefringence than disks assembled in the dark. Therefore, although light and increased temperature both enhance the rate of disk membrane assembly, they have opposite effects upon the birefringence of Xenopus rod outer segments.

Cytoskeletal functions in sensory receptors

Since the shapes of sensory receptors are so exquisitely specialized for mediating their unique functions, the cytoskeletons of sensory cells are deployed for morphogenetic and motile objectives in particularly interesting ways. Receptors erect cytoskeletal scaffolding to support two basic sorts of surface elaborations: 1) those designed to achieve the most effective presentation of specialized membrane laden with receptor proteins (photoreceptors, olfactory receptors, taste cells, and chemoreceptors), and 2) those designed to respond directly to mechanical perturbations in the cell's environment (auditory hair cells, mechanoreceptors). Each of these receptor types has specific structural requirements.Sensory receptors have built their surface elaborations upon either microtubule- or actin-based scaffoldings. Microtubule-based scaffoldings have evolved from motile cilia, and the axoneme has been modified to various ends. All ciliary-derived receptors so far described, except (curiously) those from the worm Caenorhabdites elegans, are associated with basal bodies which nucleate the assembly of surface specializations. The mechanisms for elaborating the myriad membrane specializations associated with ciliary receptors are not yet understood. Recently it has been shown that in vertebrate photoreceptors, actin is not required for the addition of membrane to the outer segment, but it is required for the proper assembly of new disks .

Experimental investigation of wave velocity and dynamic contact stresses in an assembly of disks

Dynamic photoelasticity and strain-gage techniques are employed to study wave propagation and dynamic load transfer in granular media. The granular medium is modeled as one- and two-dimensional deterministic and random arrays of circular disks of polyester material Homalite 100. The dynamic loading is achieved by explosive excitation. The experimental data are analyzed to determine the wave velocities, to identify the characteristic load transfer paths, and to quantitatively obtain the dynamic contact forces in the granular assembly. It is observed that the wave-propagation and dynamic-load-transfer phenomenon depends on the disk diameter and the obliqueness and flexibility of the load-transfer paths. The wave speed drops significantly in the first few granules after which the decay is more gradual. The load transter is characterized by the contact length and the friction between the contacting granules. The peak loads drop as the distance of the contact points from the point of explosive loading increases. For two-dimensional wave propagation, the load-transfer paths and the magnitude of contacting forces depend on the angles made by the normals of the contacting disks at the contact point.

The role of floe collisions in sea ice rheology

A collisional rheology for an idealized two‐dimensional flow of a fragmented ice field is derived. This fragmented ice field is modeled as an assembly of identical smooth disks. Collisions between neighboring disks are caused by the mean deformation field. These collisions transfer momentum which produces the internal stresses in the deforming ice field. By equating the collisional energy losses to the deformational energy, a relationship between the stress and strain rate is quantified. To demonstrate the essential idea, an analytical derivation is first given under quite restricted assumptions. A Monte Carlo simulation is then developed to provide a more general approach for the analysis. It is found that the collisional stresses are proportional to the square of disk diameter and the square of the deformation rate. The magnitude of stresses is also found to increase rapidly as the collisional restitution of disks increases, the collisional rheology yields zero tensile strength. The associated normal flow rule commonly used in the plastic rheology is not valid in the collisional rheology. It is found that the collisional stresses are very small. Consequently, the resulting stress divergence is estimated to be much lower than the air stress typically encountered in the marginal ice zone. However, these collisional stresses become singular as the maximum compactness is reached, indicating that a different mechanism may exist in that extreme.

Light scattering from dielectric targets composed of a continuous assembly of circular disks

A technique for computing the electromagnetic fields scattered by spheres, cylinders, spheroids, spirals, toroids, and other targets which can be subdivided into circular disks is given. First-order calculations are performed for targets the size and refractive index of which preclude the creation of standing waves within the target. It is found that the scattering signatures of these various shapes are distinguishable for wavelengths larger than the target, but the differences rapidly diminish, as expected, with increasing wavelength. Finite cylinders are compared to prolate spheroids of equal volume, toroids are compared with oblate spheroids of equal volume, and calculations of the CIDS ratio for a spiral target are made for various wavelengths. It is found, on comparing these spiral calculations to other work on essentially 1-D spirals, that giving the spiral wire even a very small radius significantly affects the CIDS pattern for backscattering.

Percolation threshold of a random array of discs: a numerical simulation

The authors evaluate numerically the percolation threshold of a 3D assembly of widthless monodisperse discs (radius R, number per unit volume N) in terms of the quasi-invariant NR. The value obtained is consistent with previous estimates. This model should apply to the permeability problem of fractured rocks.

A criterion for percolation threshold in a random array of plates

We give a dimensionless criterion for percolation of a random assembly of 3-dimensional flat disks of radius r with a density N per unit volume as ( Nr 3) c ∼0.15 to 0.3. The invariant at threshold is obtained by analogy with excluded volume results for arrays of needles or with the active filling factor approach used for spheres. As the result can be applied to the permeability of fractured rocks, we discuss the results for polydisperse assemblies and we show how the invariant can be measured from a random cut of the array of disks.

A discrete numerical model for granular assemblies

The distinct element method is a numerical model capable of describing the mechanical behaviour of assemblies of discs and spheres. The method is based on the use of an explicit numerical scheme in which the interaction of the particles is monitored contact by contact and the motion of the particles modelled particle by particle. The main features of the distinct element method are described. The method is validated by comparing force vector plots obtained from the computer program BALL with the corresponding plots obtained from a photoelastic analysis. The photoelastic analysis used for the comparison is the one applied to an assembly of discs by De Josselin de Jong and Verruijt (1969). The force vector diagrams obtained numerically closely resemble those obtained photoelastically. It is concluded from this comparison that the distinct element method and the program BALL are valid tools for research into the behaviour of granular assemblies. La méthode des éléments distincts est un modèle numérique capable de décrire le comportement mécanique de l'assemblage de disques et de sphères. La méthode est basée sur l'utilisation d'un système numérique explicite dans lequel l'interaction des particules est contrôlée contact par contact et le mouvement des particules simulé particule par particule. Les caracteristiques principales de la méthode des eléments distints sont décrites. La méthode est validée en comparant les tracés de vecteur de force obtenus par le programme sur ordicateur BALL avec les tracés correspondants obtanus a l'aide d'une analyse photo-élastique. L'analyse photo-élastique utilisée pour la comparaison est celle appliquée sur un assemblage de disques par De Josselin de Jong et Verruijt (1969). Les diagrammes de vecteur de force obtenus numériquement sont très voisins de ceux obtenus photo-élastiquement. Cette comparaison permet de conclure que la methode des éléments distincts et le programme BALL sont des instruments valables pour la recherche du comportement des assemblages granulaires.

Modern theories of liquids and the diffuse equatorial X-ray scattering from collagen

The idea that the lateral arrangement of a proportion of molecules in the collagen fibril displays a short-range two-dimensional liquid-like order is investigated and shown to be true. Theoretical calculations of a dense disordered assembly of hard discs yield X-ray scattering curves which possess the features of the near equatorial diffuse scattering from rat-tail tendon collagen. The theoretical model used is the integral equation formulation of Percus & Yevick [Phys. Rev. (1958). 110, 1] known to be almost exact for hard-disc potentials. The molecular diameter and number density of molecules obtained from the comparison with experiment are close to those suggested by Woodhead-Galloway, Hukins & Wray [Biochem. Biophys. Res. Commun. (1975). 64, 1237-1244] to explain the ordered part of the collagen and to those suggested by Katz & Li [J. Mol. Biol. (1973). 73, 351-369] on the basis of an investigation of the density of wet tendon. A brief discussion of elastoidin is included. Discrepancies between the observed and predicted scattering are discussed.

The photoreceptors of diurnal squirrels: Outer segment structure, disc shedding, and protein renewal

The photoreceptor outer segments of five species of diurnal squirrels were studied by light and electron microscopy. In all species rod outer segments could be distinguished from cone outer segments by the extent of disc-membrane continuity and by their pattern of protein renewal as determined by autoradiography. Rods showed the characteristic band of radioactive protein within the outer segments, while the cones showed only a diffuse pattern of outer segment labeling. Rod as well as cone outer segments were found to shed packets of discs intermittently. The shedding process appeared to be qualitatively similar in rods and cones. Multiple invaginations of the outer membrane, probably signifying the assembly of new discs, were detected at the base of rod outer segments. Single partially formed invaginations, analogous to those found in rods, also were found at the base of cone outer segments. Thus, cone as well as rod outer segments may assemble and shed discs in the mature animal.

Photoelastic verification of a mechanical model for the flow of a granular material

T his paper describes experiments performed on an assembly of discs constituting a two-dimensional analogue of a granular material. The use of photo-elasticity techniques allows the determination of average stress and strain-rate tensors in the interior of the assembly. In this way, a comparison can be made with the behaviour predicted theoretically on the basis of a mechanical model. Test results indicate that the main features of the mechanical model, namely, the sub-division of the assembly into sliding elements, a possible non-coaxiality of stress and strain-rate tensors, and a free rotation of the elements are all indeed observed in practice.

THE RENEWAL OF ROD AND CONE OUTER SEGMENTS IN THE RHESUS MONKEY

The renewal of retinal rod and cone outer segments has been studied by radioautography in rhesus monkeys examined 2 and 4 days after injection of leucine-(3)H. The cell outer segment consists of a stack of photosensitive, membranous discs. In both rods and cones some of the newly formed (radioactive) protein became distributed throughout the outer segment. Furthermore, in rods (but not in cones), there was a transverse band of concentrated radioactive protein slightly above the outer segment base 2 days after injection. This was due to the formation of new discs, into which labeled protein had been incorporated. At 4 days, these radioactive discs were located farther from the outer segment base. Repeated assembly of new discs had displaced them away from the basal assembly site and along the outer segment. Measurements of the displacement rate indicated that each retinal rod produces 80-90 discs per day, and that the entire complement of outer segment discs is replaced every 9-13 days. To compensate for the continual formation of new discs, groups of old discs are intermittently shed from the apical end of the cell and phagocytized by the pigment epithelium. Each pigment epithelial cell engulfs and destroys about 2000-4000 rod outer segment discs daily. The similarity between visual cells in the rhesus monkey and those in man suggests that the same renewal processes occur in the human retina.

Shedding of discs from rod outer segments in the rhesus monkey

Renewal of the photosensitive outer segment of rod visual cells involves the continued assembly of new membranous discs accompanied by a balanced loss and destruction of old disc material. The process by which the old discs are detached from the rod outer segments in the retina of the rhesus monkey has been studied by electron microscopy. Discs are shed from the end of the cylindrical segment in groups generally containing 8–30 discs. The endmost discs curl up at the edge, displacing a small amount of cytoplasm into the space thereby created. The outer rod membrane then folds into the zone separating the deformed discs from the remainder of the outer segment. This serves to dissect away the terminal discs while reforming the membrane over the tip of the cell. Next, the shed discs are surrounded by cytoplasmic extensions from the pigment epithelium and withdrawn into the body of that cell within a phagosome.