The origin of polygonal troughs on the Northern Plains of Mars

Viking photographs have revealed extraordinary systems of crudely polygonal troughs in three different areas of the northern plains of Mars. Trough widths average 200–800 m and average trough spacing is 5–10 km. The widest troughs have flat floors and steep sides which suggest that they are either grabens or tension cracks which have been partially filled. The following three arguments support the garben interpretation: (1) Two clear examples of vertical offsets along trough walls indicate that the troughs formed by downdropping of the floors. (2) Troughs similar in scale and morphology to those of the Martian northern plains form concentric and radial patterns in the Caloris Basin on Mercury. Most likely, they are extensional fractures or grabens resulting from uplift of the basin floor (Strom et al., 1975). The Caloris analogy suggests that the troughs on Mars are similar tectonic features related either to uplift or expansion of the planet. Fourteen rose diagrams of trough azimuths in southeastern Acidalia Planita show that locally they exhibit preferred orientations roughly parallel to the topographic contours, but overall there is no strong regional pattern. (3) The scale of tension crack systems is limited by the depth of fracturing because the extent of stress relief perpendicular to a crack is proportional to the crack depth. Observations of terrestrial tension cracks suggest a lower limit on crack depths of about one-tenth of the average spacing. Thus, if the Martian troughs are tension cracks, they would be expected to have depths of at least 500–1000 m. Mechanical considerations indicate that it is difficult to generate such deep cracks by surficial tension due to thermal cooling and contraction in permafrost, desiccation, or cooling of lava flows. Deep-seated tension of tectonic origin generally results in normal faults and not tension cracks.     

A numerical study of aerosol growth in Titan's atmosphere

We present a simple model for the formation and growth of photochemical aerosols in the atmosphere of Titan. We show that, in general, an optically thick layer of particles in the size range required by models of Titan cannot be obtained at pressures less than about 2 mbar. Since the thin model of Titan's atmosphere requires that the inversion not extend below pressures of 0.11 mbar (D. M. Hunten and J. J. Caldwell, 1978, preprint), it seems to be ruled out by the calculations.     

The quasi integrals

The usual Von Zeipel transformations of the Hamiltonian Mechanics are presented, they lead to state functions with extremely slow variations: the quasi-integrals.The Von Zeipel transformations are implicit: an explicit and direct construction of the quasi-integrals is also presented and the quasi-invariance property of these functions is demonstrated.These results are applied to the problem of the motion of artificial satellites perturbed by the zonal harmonics of the Earth potential, the quasi-integral is given, it is then so constant that the problem can be considered as integrable.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.     

Heat flow near obstacles in the solar convection zone

Disturbances in the heat flow in the solar convection zone are calculated with a turbulent thermal diffusion coefficient based on a mixing length approximation. As a consequence of the radiative boundary condition at the surface and the strong increase of the diffusion coefficient with depth, the convection zone resembles a thermally superconducting shell enclosed between a thin surface layer and an interior core of low thermal conductivity. Thermal disturbances originating in the convection zone do not penetrate into the interior, and penetrate only weakly through the solar surface. A thermally isolating obstacle buried entirely in the convection zone casts a shadow of reduced temperature at the solar surface; the brightening surrounding this shadow is undetectable. The shadow is weak unless the object is located close to the surface (less than 2000 km). Assuming a sunspot to be an area of reduced thermal conductivity which extends a finite depth into the convection zone, the heat flow around this obstacle is calculated. The heat flux blocked below the spot (missing flux) spreads over a very extended area surrounding the spot. The brightening corresponding to this missing flux is undetectable if the reduction of the thermal conductivity extends to a depth greater than 1000 km. It is concluded that no effect other than a decrease of the convective efficiency is needed to explain the temperature change observed at the solar surface in and around a sunspot. The energy balance is calculated between magnetic flux tubes, oriented vertically in the solar surface, (magnetic elements in active regions and the quiet network) and their surroundings. Near the visible surface radiation enters the tube laterally from the surrounding convection zone. The heating effect of this influx is important for small tubes (less than a few arcseconds). Due to this influx tubes less than about 1 in diameter can appear as bright structures irrespective of the amount of heat conveyed along the tube itself. Through the lateral influx, small tubes such as are found in the quiet network act as little leaks in the solar surface through which an excess heat flux escapes from the convection zone.     

Newtonian cosmology with a varying gravitational constant

Newtonian cosmology is developed with the assumption that the gravitational constantG diminishes with time. The functional form adopted forG(t), a modification of a suggestion of Dirac, isG=A(k+t) ^–1, wheret is the age of the Universe and a small constantk is inserted to avoid a singularity in the two-body problem. IfR is the scale factor, normalized to unity at an epoch time , the differential equation is then . Here ₀ is the mean density at the epoch time. With the above form forG(t), the solution is reducible to quadratures.The scale factorR either increases indefinitely or has one and only one maximum. LetH ₀ be the present value of Hubble's constant /R and _0c the minimum density for a maximum ofR, i.e., for closure of the Universe. The conditions for a maximum lead to a boundary curve of _0c versusH ₀ and the numbers indicate strongly that thisG-variable Newtonian model corresponds to an open universe. An upward estimate of the age of the Universe from 10¹⁰ yr to five times such a value would still lead to the same conclusion.The present Newtonian cosmology appears to refute the statement, sometimes made, that the Dirac model forG necessarily leads to the conclusion that the age of the Universe is one-third the Hubble time. Appendix B treats this point, explaining that this incorrect conclusion arises from using all the assumptions in Dirac (1938). The present paper uses only Dirac's final result, viz,G(k+t)^–1, superposing it on the differential equation .     

Magnetic disturbance effects in the E region of the ionosphere

Detailed studies of the daytime E-region critical frequency at Aberystwyth (geomagnetic latitude +56°) show clear evidence for changes associated with both the axially-symmetric (Dst) and asymmetric (DS) components of the disturbance magnetic field. Comparison of the sensitivity of the E-region peak density to these two influences shows that the changes cannot entirely (if at all) be ascribed to the influence of electric currents in the region. It is suggested that a major role is played by dynamical influences associated with the neutral air “storm circulation” which distributes the energy fed into the auroral region to lower latitudes.     

Laboratory simulation of volatilisation from melts induced by micrometeoroid impacts

The laboratory simulation experiments on volatilization from the melts formed due to micrometeoroid impacts on the lunar surface were carried out. The simulation was performed using modulated laser pulses incident on rocks and minerals in vacuum; in so doing microcraters on the targets, glass particles, condensates were formed and gases solved in the bulk of the rock and mineral grains were released. It is shown that volatilization from only the crater glass layers is negligible, which fully confirms the theoretical predictions of Nussinov and Chernyak.The volatilizations from the drops formed by the micrometeoric impacts can be noticeable. For micron-sized drops, predominant among the others after the impact, the volatilization of Na, K and other volatiles can be up to 10 to 20%. For larger-sized (d10² m) drops the volatilization should lead to the appearance of the significant gradients of the element concentrations over the particle cross-section and as a result of their normalization it leads to the surface enrichment by some elements (Si and others).The mechanism of dust formation due to the surface rocks attack by volatilizing alkaline metals (Naughtonet al.) on the Moon probably is not effective. It is the consequence of such a fact that the condensate of the target materials evaporated due to other simultaneous micrometeoric impacts and had the same (as the target has) elemental composition is the very strong background for volatilizing and condensating alkaline elements.Preliminary conclusions about a possible correlation between the composition and the sizes of dust particles in the Solar system and in the Universe (at similar initial composition) have been drawn.     

Shear-induced instability and arch filament eruption: A magnetohydrodynamic (MHD) numerical simulation

We investigate, via a two-dimensional (nonplanar) MHD simulation, a situation wherein a bipolar magnetic field embedded in a stratified solar atmosphere (i.e., arch-filament-like structure) undergoes symmetrical shear motion at the footpoints. It was found that the vertical plasma flow velocities grow exponentially leading to a new type of global MHD-instability that could be characterized as a Dynamic Shearing Instability, with a growth rate of about 8{ovV} _A a, where {ovV} _A is the average Alfvén speed and a ^–1 is the characteristic length scale. The growth rate grows almost linearly until it reaches the same order of magnitude as the Alfvén speed. Then a nonlinear MHD instability occurs beyond this point. This simulation indicates the following physical consequences: the central loops are pinched by opposing Lorentz forces, and the outer closed loops stretch upward with the vertically-rising mass flow. This instability may apply to arch filament eruptions (AFE) and coronal mass ejections (CMEs).To illustrate the nonlinear dynamical shearing instability, a numerical example is given for three different values of the plasma beta that span several orders of magnitude. The numerical results were analyzed using a linearized asymptotic approach in which an analytical approximate solution for velocity growth is presented. Finally, this theoretical model is applied to describe the arch filament eruption as well as CMEs.