Relationship, through geologic time, of days per lunar month to growth increments in fossil and recent molluscan shells Semiannual status report, 14 Sep. 1967 - 14 Mar. 1968

Relationship of geologic time and days per lunar month to growth patterns in fossil and recent molluscan shell

The Abundance of Molecular Hydrogen and its Correlation with Midplane Pressure in Galaxies: Non-Equilibrium, Turbulent, Chemical Models

Observations of spiral galaxies show a strong linear correlation between the ratio of molecular to atomic hydrogen surface density R_mol and midplane pressure. To explain this, we simulate three-dimensional, magnetized turbulence, including simplified treatments of non-equilibrium chemistry and the propagation of dissociating radiation, to follow the formation of H_2 from cold atomic gas. The formation time scale for H_2 is sufficiently long that equilibrium is not reached within the 20-30 Myr lifetimes of molecular clouds. The equilibrium balance between radiative dissociation and H_2 formation on dust grains fails to predict the time-dependent molecular fractions we find. A simple, time-dependent model of H_2 formation can reproduce the gross behavior, although turbulent density perturbations increase molecular fractions by a factor of few above it. In contradiction to equilibrium models, radiative dissociation of molecules plays little role in our model for diffuse radiation fields with strengths less than ten times that of the solar neighborhood, because of the effective self-shielding of H_2. The observed correlation of R_mol with pressure corresponds to a correlation with local gas density if the effective temperature in the cold neutral medium of galactic disks is roughly constant. We indeed find such a correlation of R_mol with density. If we examine the value of R_mol in our local models after a free-fall time at their average density, as expected for models of molecular cloud formation by large-scale gravitational instability, our models reproduce the observed correlation over more than an order of magnitude range in density.Comment: 24 pages, 4 figures, accepted for publication in Astrophys. J, changes include addition of models with higher radiation fields and substantial clarification of the narrativ

Applications of inertial navigation and modern control theory to the all weather landing problem

Inertial navigation and automatic landing control theory applied to instrument landing proble

Ultrasensitivity in phosphorylation-dephosphorylation cycles with little substrate

Cellular decision-making is driven by dynamic behaviours, such as the preparations for sunrise enabled by circadian rhythms and the choice of cell fates enabled by positive feedback. Such behaviours are often built upon ultrasensitive responses where a linear change in input generates a sigmoidal change in output. Phosphorylation-dephosphorylation cycles are one means to generate ultrasensitivity. Using bioinformatics, we show that in vivo levels of kinases and phosphatases frequently exceed the levels of their corresponding substrates in budding yeast. This result is in contrast to the conditions often required by zero-order ultrasensitivity, perhaps the most well known means for how such cycles become ultrasensitive. We therefore introduce a mechanism to generate ultrasensitivity when numbers of enzymes are higher than numbers of substrates. Our model combines distributive and non-distributive actions of the enzymes with two-stage binding and concerted allosteric transitions of the substrate. We use analytical and numerical methods to calculate the Hill number of the response. For a substrate with [Formula: see text] phosphosites, we find an upper bound of the Hill number of [Formula: see text], and so even systems with a single phosphosite can be ultrasensitive. Two-stage binding, where an enzyme must first bind to a binding site on the substrate before it can access the substrate's phosphosites, allows the enzymes to sequester the substrate. Such sequestration combined with competition for each phosphosite provides an intuitive explanation for the sigmoidal shifts in levels of phosphorylated substrate. Additionally, we find cases for which the response is not monotonic, but shows instead a peak at intermediate levels of input. Given its generality, we expect the mechanism described by our model to often underlay decision-making circuits in eukaryotic cells

The geometry of extended null supersymmetry in M-theory

For supersymmetric spacetimes in eleven dimensions admitting a null Killing spinor, a set of explicit necessary and sufficient conditions for the existence of any number of arbitrary additional Killing spinors is derived. The necessary and sufficient conditions are comprised of algebraic relationships, linear in the spinorial components, between the spinorial components and their first derivatives, and the components of the spin connection and four-form. The integrability conditions for the Killing spinor equation are also analysed in detail, to determine which components of the field equations are implied by arbitrary additional supersymmetries and the four-form Bianchi identity. This provides a complete formalism for the systematic and exhaustive investigation of all spacetimes with extended null supersymmetry in eleven dimensions. The formalism is employed to show that the general bosonic solution of eleven dimensional supergravity admitting a $G_2$ structure defined by four Killing spinors is either locally the direct product of $\mathbb{R}^{1,3}$ with a seven-manifold of $G_2$ holonomy, or locally the Freund-Rubin direct product of $AdS_4$ with a seven-manifold of weak $G_2$ holonomy. In addition, all supersymmetric spacetimes admitting a $(G_2\ltimes\mathbb{R}^7)\times\mathbb{R}^2$ structure are classified.Comment: 36 pages, latex; v2, section classifying all spacetimes admitting a $(G_2\ltimes\mathbb{R}^7)\times\mathbb{R}^2$ structure included; v3, typos corrected. Final version to appear in Phys.Rev.

Fast Molecular Cloud Destruction Requires Fast Cloud Formation

A large fraction of the gas in the Galaxy is cold, dense, and molecular. If all this gas collapsed under the influence of gravity and formed stars in a local free-fall time, the star formation rate in the Galaxy would exceed that observed by more than an order of magnitude. Other star-forming galaxies behave similarly. Yet observations and simulations both suggest that the molecular gas is indeed gravitationally collapsing, albeit hierarchically. Prompt stellar feedback offers a potential solution to the low observed star formation rate if it quickly disrupts star-forming clouds during gravitational collapse. However, this requires that molecular clouds must be short-lived objects, raising the question of how so much gas can be observed in the molecular phase. This can occur only if molecular clouds form as quickly as they are destroyed, maintaining a global equilibrium fraction of dense gas. We therefore examine cloud formation timescales. We first demonstrate that supernova and superbubble sweeping cannot produce dense gas at the rate required to match the cloud destruction rate. On the other hand, Toomre gravitational instability can reach the required production rate. We thus argue that, although dense, star-forming gas may last only around a single global free-fall time, the dense gas in star-forming galaxies can globally exist in a state of dynamic equilibrium between formation by gravitational instability, and disruption by stellar feedback. At redshift z >~ 2, the Toomre instability timescale decreases, resulting in a prediction of higher molecular gas fractions at early times, in agreement with observations.Comment: 7 pages, no figures, ApJL accepted; v3: corrected several errors, added discussion, no change in conclusion

Nimbus power systems /1960 - 1969/

Power supply subsystems for use on Nimbus satellite progra

Temperature Fluctuations driven by Magnetorotational Instability in Protoplanetary Disks

The magnetorotational instability (MRI) drives magnetized turbulence in sufficiently ionized regions of protoplanetary disks, leading to mass accretion. The dissipation of the potential energy associated with this accretion determines the thermal structure of accreting regions. Until recently, the heating from the turbulence has only been treated in an azimuthally averaged sense, neglecting local fluctuations. However, magnetized turbulence dissipates its energy intermittently in current sheet structures. We study this intermittent energy dissipation using high resolution numerical models including a treatment of radiative thermal diffusion in an optically thick regime. Our models predict that these turbulent current sheets drive order unity temperature variations even where the MRI is damped strongly by Ohmic resistivity. This implies that the current sheet structures where energy dissipation occurs must be well resolved to correctly capture the flow structure in numerical models. Higher resolutions are required to resolve energy dissipation than to resolve the magnetic field strength or accretion stresses. The temperature variations are large enough to have major consequences for mineral formation in disks, including melting chondrules, remelting calcium-aluminum rich inclusions, and annealing silicates; and may drive hysteresis: current sheets in MRI active regions could be significantly more conductive than the remainder of the disk.Comment: 16 pages, 13 figures, ApJ In Press, updated to match proof

Determination of Shapes of Boattail Bodies of Revolution for Minimum Wave Drag

By use of an approximate equation for the wave drag of slender bodies of revolution in a supersonic flow field, the optimum shapes of certain boattail bodies are determined for minimum wave drag. The properties of three specific families of bodies are determined, the first family consisting of bodies having a given length and base area and a contour passing through a prescribed point between the nose and base, the second family having fixed length, base area, and maximum area, and the third family having given length, volume, and base area. The method presented is easily generalized to determine minimum-wave-drag profile shapes which have contours that must pass through any prescribed number of points. According to linearized theory, the optimum profiles are found to have infinite slope at the nose but zero radius of curvature so that the bodies appear to have pointed noses, a zero slope at the body base, and no variation of wave drag with Mach number. For those bodies having a specified intermediate.diameter (that is, location and magnitude given), the maximum body diameter is shown to be larger, in general, than the specified diameter. It is also shown that, for bodies having a specified maximum diameter, the location of the maximum diameter is not arbitrary but is determined from the ratio of base diameter to maximum diameter