Spatial linear global instability analysis of the HIFiRE-5 elliptic cone model flow

The linear instability of the three-dimensional boundary-layer over the HIFiRE-5 flight test geometry, i.e. a rounded-tip 2:1 elliptic cone, at Mach 7, has been analyzed through spatial BiGlobal analysis, in a effort to understand transition and accurately predict local heat loads on next-generation ight vehicles. The results at an intermediate axial section of the cone, Re x = 8x10 5, show three different families of spatially amplied linear global modes, the attachment-line and cross- ow modes known from earlier analyses, and a new global mode, peaking in the vicinity of the minor axis of the cone, termed \center-line mode". We discover that a sequence of symmetric and anti-symmetric centerline modes exist and, for the basic ow at hand, are maximally amplied around F* = 130kHz. The wavenumbers and spatial distribution of amplitude functions of the centerline modes are documented

Accurate Parabolic Navier-Stokes solutions of the supersonic flow around and elliptic cone

Flows of relevance to new generation aerospace vehicles exist, which are weakly dependent on the streamwise direction and strongly dependent on the other two spatial directions, such as the flow around the (flattened) nose of the vehicle and the associated elliptic cone model. Exploiting these characteristics, a parabolic integration of the Navier-Stokes equations is more appropriate than solution of the full equations, resulting in the so-called Parabolic Navier-Stokes (PNS). This approach not only is the best candidate, in terms of computational efficiency and accuracy, for the computation of steady base flows with the appointed properties, but also permits performing instability analysis and laminar-turbulent transition studies a-posteriori to the base flow computation. This is to be contrasted with the alternative approach of using order-of-magnitude more expensive spatial Direct Numerical Simulations (DNS) for the description of the transition process. The PNS equations used here have been formulated for an arbitrary coordinate transformation and the spatial discretization is performed using a novel stable high-order finite-difference-based numerical scheme, ensuring the recovery of highly accurate solutions using modest computing resources. For verification purposes, the boundary layer solution around a circular cone at zero angle of attack is compared in the incompressible limit with theoretical profiles. Also, the recovered shock wave angle at supersonic conditions is compared with theoretical predictions in the same circular-base cone geometry. Finally, the entire flow field, including shock position and compressible boundary layer around a 2:1 elliptic cone is recovered at Mach numbers 3 and 4

A Schwarz lemma for Kahler affine metrics and the canonical potential of a proper convex cone

This is an account of some aspects of the geometry of Kahler affine metrics based on considering them as smooth metric measure spaces and applying the comparison geometry of Bakry-Emery Ricci tensors. Such techniques yield a version for Kahler affine metrics of Yau s Schwarz lemma for volume forms. By a theorem of Cheng and Yau, there is a canonical Kahler affine Einstein metric on a proper convex domain, and the Schwarz lemma gives a direct proof of its uniqueness up to homothety. The potential for this metric is a function canonically associated to the cone, characterized by the property that its level sets are hyperbolic affine spheres foliating the cone. It is shown that for an n -dimensional cone, a rescaling of the canonical potential is an n -normal barrier function in the sense of interior point methods for conic programming. It is explained also how to construct from the canonical potential Monge-Ampère metrics of both Riemannian and Lorentzian signatures, and a mean curvature zero conical Lagrangian submanifold of the flat para-Kahler space.

Disease sequence from mutant rhodopsin allele to rod and cone photoreceptor degeneration in man

Mutations in the gene encoding rhodopsin, the visual pigment in rod photoreceptors, lead to retinal degeneration in species from Drosophila to man. The pathogenic sequence from rod cell-specific mutation to degeneration of rods and cones remains unclear. To understand the disease process in man, we studied heterozygotes with 18 different rhodopsin gene mutations by using noninvasive tests of rod and cone function and retinal histopathology. Two classes of disease expression were found, and there was allele-specificity. Class A mutants lead to severely abnormal rod function across the retina early in life; topography of residual cone function parallels cone cell density. Class B mutants are compatible with normal rods in adult life in some retinal regions or throughout the retina, and there is a slow stereotypical disease sequence. Disease manifests as a loss of rod photoreceptor outer segments, not singly but in microscopic patches that coalesce into larger irregular areas of degeneration. Cone outer segment function remains normal until >75% of rod outer segments are lost. The topography of cone loss coincides with that of rod loss. Most class B mutants show an inferior-nasal to superior-temporal retinal gradient of disease vulnerability associated with visual cycle abnormalities. Class A mutant alleles behave as if cytotoxic; class B mutants can be relatively innocuous and epigenetic factors may play a major role in the retinal degeneration.

Mechanisms of spectral tuning in the mouse green cone pigment

Diversification of cone pigment spectral sensitivities during evolution is a prerequisite for the development of color vision. Previous studies have identified two naturally occurring mechanisms that produce variation among vertebrate pigments by red-shifting visual pigment absorbance: addition of hydroxyl groups to the putative chromophore binding pocket and binding of chloride to a putative extracellular loop. In this paper we describe the use of two blue-shifting mechanisms during the evolution of rodent long-wave cone pigments. The mouse green pigment belongs to the long-wave subfamily of cone pigments, but its absorption maximum is 508 nm, similar to that of the rhodopsin subfamily of visual pigments, but blue-shifted 44 nm relative to the human red pigment, its closest homologue. We show that acquisition of a hydroxyl group near the retinylidene Schiff base and loss of the chloride binding site mentioned above fully account for the observed blue shift. These data indicate that the chloride binding site is not a universal attribute of long-wave cone pigments as generally supposed, and that, depending upon location, hydroxyl groups can alter the environment of the chromophore to produce either red or blue shifts.

Semaphorin 3A growth cone collapse requires a sequence homologous to tarantula hanatoxin

Axonal guidance is key to the formation of neuronal circuitry. Semaphorin 3A (Sema 3A; previously known as semaphorin III, semaphorin D, and collapsin-1), a secreted subtype of the semaphorin family, is an important axonal guidance molecule in vitro and in vivo. The molecular mechanisms of the repellent activity of semaphorins are, however, poorly understood. We have now found that the secreted semaphorins contain a short sequence of high homology to hanatoxin, a tarantula K+ and Ca2+ ion channel blocker. Point mutations in the hanatoxin-like sequence of Sema 3A reduce its capacity to repel embryonic dorsal root ganglion axons. Sema 3A growth cone collapse activity is inhibited by hanatoxin, general Ca2+ channel blockers, a reduction in extracellular or intracellular Ca2+, and a calmodulin inhibitor, but not by K+ channel blockers. Our data support an important role for Ca2+ in mediating the Sema 3A response and suggest that Sema 3A may produce its effects by causing the opening of Ca2+ channels.

An alternative pathway for rod signals in the rodent retina: Rod photoreceptors, cone bipolar cells, and the localization of glutamate receptors

In the mammalian retina, extensive processing of spatiotemporal and chromatic information occurs. One key principle in signal transfer through the retina is parallel processing. Two of these parallel pathways are the ON- and OFF-channels transmitting light and dark signals. This dual system is created in the outer plexiform layer, the first relay station in retinal signal transfer. Photoreceptors release glutamate onto ON- and OFF-type bipolar cells, which are functionally distinguished by their postsynaptic expression of different types of glutamate receptors, namely ionotropic and metabotropic glutamate receptors. In the current concept, rod photoreceptors connect only to rod bipolar cells (ON-type) and cone photoreceptors connect only to cone bipolar cells (ON- and OFF-type). We have studied the distribution of (RS)-α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) glutamate receptor subunits at the synapses in the outer plexiform layer of the rodent retina by immunoelectron microscopy and serial section reconstruction. We report a non-classical synaptic contact and an alternative pathway for rod signals in the retina. Rod photoreceptors made synaptic contact with putative OFF-cone bipolar cells that expressed the AMPA glutamate receptor subunits GluR1 and GluR2 on their dendrites. Thus, in the retina of mouse and rat, an alternative pathway for rod signals exists, where rod photoreceptors bypass the rod bipolar cell and directly excite OFF-cone bipolar cells through an ionotropic sign-conserving AMPA glutamate receptor.

Horizontal cells reveal cone type-specific adaptation in primate retina

The human cone visual system maintains contrast sensitivity over a wide range of ambient illumination, a property known as light adaptation. The first stage in light adaptation is believed to take place at the first neural step in vision, within the long, middle, and short wavelength sensitive cone photoreceptors. To determine the properties of adaptation in primate outer retina, we measured cone signals in second-order interneurons, the horizontal cells, of the macaque monkey. Horizontal cells provide a unique site for studying early adaptational mechanisms; they are but one synapse away from the photoreceptors, and each horizontal cell receives excitatory inputs from many cones. Light adaptation occurred over the entire range of light levels evaluated, a luminance range of 15–1,850 trolands. Adaptation was demonstrated to be independent in each cone type and to be spatially restricted. Thus, in primates, a major source of sensitivity regulation occurs before summation of cone signals in the horizontal cell.

Radixin Is Involved in Lamellipodial Stability during Nerve Growth Cone Motility

Immunocytochemistry and in vitro studies have suggested that the ERM (ezrin-radixin-moesin) protein, radixin, may have a role in nerve growth cone motility. We tested the in situ role of radixin in chick dorsal root ganglion growth cones by observing the effects of its localized and acute inactivation. Microscale chromophore-assisted laser inactivation (micro-CALI) of radixin in growth cones causes a 30% reduction of lamellipodial area within the irradiated region whereas all control treatments did not affect lamellipodia. Micro-CALI of radixin targeted to the middle of the leading edge often split growth cones to form two smaller growth cones during continued forward movement (>80%). These findings suggest a critical role for radixin in growth cone lamellipodia that is similar to ezrin function in pseudopodia of transformed fibroblasts. They are consistent with radixin linking actin filaments to each other or to the membrane during motility.

Microtubule reorganization is obligatory for growth cone turning

To examine the role of microtubules in growth cone turning, we have compared the microtubule organization in growth cones advancing on uniform laminin substrates with their organization in growth cones turning at a laminin–tenascin border. The majority (82%) of growth cones on laminin had a symmetrical microtubule organization, in which the microtubules entering the growth cone splay out toward the periphery of the growth cone. Growth cones at tenascin borders had symmetrically arranged microtubules in only 34% of cases, whereas in the majority of cases the microtubules were displaced toward one-half of the growth cone, presumably stabilizing in the direction of the turn along the tenascin border. These results suggest that reorganization of microtubules could underlie growth cone turning. Further evidence for the involvement of microtubule rearrangement in growth cone turning was provided by experiments in which growth cones approached tenascin borders in the presence of nanomolar concentrations of the microtubule stabilizing compound, Taxol. Taxol altered the organization of microtubules in growth cones growing on laminin by restricting their distribution to the proximal regions of the growth cone and increasing their bundling. Taxol did not stop growth cone advance on laminin. When growing in the presence of Taxol, growth cones at tenascin borders were not able to turn and grow along the laminin–tenascin border, and consequently stopped at the border. Growth cones were arrested at borders for as long as Taxol was present (up to 6 h) without showing any signs of drug toxicity. These effects of Taxol were reversible. Together, these results suggest that microtubule reorganization in growth cones is a necessary event in growth cone turning.