The formation of Ganymede's grooved terrain: Numerical modeling of extensional necking instabilities

Ganymede's grooved terrain likely formed during an epoch of global expansion, when unstable extension of the lithosphere resulted in the development of periodic necking instabilities. Linear, infinitesimal-strain models of extensional necking support this model of groove formation, finding that the fastest growing modes of an instability have wavelengths and growth rates consistent with Ganymede's grooves. However, several questions remain unanswered, including how nonlinearities affect instability growth at large strains, and what role instabilities play in tectonically resurfacing preexisting terrain. To address these questions we numerically model the extension of an icy lithosphere to examine the growth of periodic necking instabilities over a broad range of strain rates and temperature gradients. We explored thermal gradients up to 45 K km⁻¹ and found that, at infinitesimal strain, maximum growth rates occur at high temperature gradients (45 K km⁻¹) and moderate strain rates (10⁻¹³ s⁻¹). Dominant wavelengths range from 1.8 to 16.4 km (post extension). Our infinitesimal growth rates are qualitatively consistent with, but an order of magnitude lower than, previous linearized calculations. When strain exceeds ∼10% growth rates decrease, limiting the total amount of amplification that can result from unstable extension. This fall-off in growth occurs at lower groove amplitudes for high-temperature-gradient, thin-lithosphere simulations than for low-temperature-gradient, thick-lithosphere simulations. At large strains, this shifts the ideal conditions for producing large amplitude grooves from high temperature gradients to more moderate temperature gradients (15 K km⁻¹). We find that the formation of periodic necking instabilities can modify preexisting terrain, replacing semi-random topography up to 100 m in amplitude with periodic ridges and troughs, assisting the tectonic resurfacing process. Despite this success, the small topographic amplification produced by our model presents a formidable challenge to the necking instability mechanism for groove formation. Success of the necking instability mechanism may require rheological weakening or strain localization by faulting, effects not included in our analysis.     

An evolutionary algorithm for multicriteria path optimization problems

For many years researchers and decision makers (DMs) faced with multicriteria shortest path problems (MSPPs) have resorted to reductions to the classical shortest path problem (SPP) by means of weighted linear combinations of the criteria. Algorithmic and approximation schemes are available to solve MSPPs but these approaches often display complexities prohibitive to their implementation on real‐world applications. This paper describes the development of an Evolutionary Algorithm (EA) approach to MSPPs on networks with multiple independent criteria. The EA approach is shown to sufficiently explore the underlying network space, generate large candidate path sets, and evolve high quality approximations to the optimal MSPP solution(s). Opportunities for early termination of the EA in time‐critical applications are also offered. Among the issues for further work is the integration of the EA as a tool within a GIS for path optimization.     

Inventory of nonvolatile fatty acids and hydrocarbons in the oceans

A survey of the distribution of nonvolatile fatty acids and hydrocarbons in the oceans is given. The results represent more a “feel” from the literature rather than a mathematical analysis and are given in Table III. Fatty acid concentration appears to show a greater variation, presumably because they are more prone to biological influences than the hydrocarbons.     

Viscous damping of nonlinear magneto-acoustic waves

The motivation for the present work is discussed, and in Section 2 the nonlinear Burger's equation is derived for wave propagation in a compressible unstratified viscous fluid permeated by a magnetic field (initially constant), using the reductive perturbation method of Taniuti and Wei (1968). An analytic solution of the equation is given (after Sakai, 1972) and the angular behaviour is shown for certain parameters describing the nonlinearity and damping of the system, for both fast- and slow-mode disturbances.     

Maximum growth rates of magnetoatmospheric instabilities

Simple bounds on the growth rates of magneto-atmospheric instabilities are derived, both for perturbations along and perpendicular to a horizontal magnetic field. The physical significance of a singular level for stable modes is briefly discussed.     

Can a dam type of an alpine lake be derived from lake geometry?A negative result

Glacial lake outburst floods(GLOFs)represent one of the most serious hazard and risk in deglaciating high mountain regions worldwide and the need for GLOF hazard and risk assessment is apparent.As a consequence,numerous region-and nation-wide GLOF assessment studies have been published recently.These studies cover large areas and consider hundreds to thousands of lakes,prioritizing the hazard posed by them.Clearly,certain simplification is required for executing such studies,often resulting in neglecting qualitative characteristics which would need manual assignment.Different lake dam types(e.g.,bedrock-dammed,moraine-dammed)are often not distinguished,despite they control GLOF mechanism(dam overtopping/dam breach)and thus GLOF magnitude.In this study,we explore the potential of easily measurable quantitative characteristics and four ratios to approximate the lake dam type.Our dataset of 851 lakes of the Cordillera Blanca suggests that while variances and means of these characteristics of individual lake types differ significantly(F-test,t-test),value distribution of different geometrical properties can’t be used for the originally proposed purpose along the spectra.The only promising results are obtained for extreme values(selected bins)of the ratios.For instance,the low width to length ratio indicates likely morainedammed lake while the high value of ratio indicating round-shape of the lake indicates increased likelihood of bedrock-dammed lake.Overall,we report a negative result of our experiment since there are negligible differences of relative frequencies in most of the bins along the spectra.     

Coupled convection and tidal dissipation in Europa’s ice shell

We performed 2D numerical simulations of oscillatory tidal flexing to study the interrelationship between tidal dissipation (calculated using the Maxwell model) and a heterogeneous temperature structure in Europa’s ice shell. Our 2D simulations show that, if the temperature is spatially uniform, the tidal dissipation rate peaks when the Maxwell time is close to the tidal period, consistent with previous studies. The tidal dissipation rate in a convective plume encased in a different background temperature depends on both the plume and background temperature. At a fixed background temperature, the dissipation increases strongly with plume temperature at low temperatures, peaks, and then decreases with temperature near the melting point when a melting-temperature viscosity of 10¹³ Pa s is used; however, the peak occurs at significantly higher temperature in this heterogeneous case than in a homogeneous medium for equivalent rheology. For constant plume temperature, the dissipation rate in a plume decreases as the surrounding temperature increases; plumes that are warmer than their surroundings can exhibit enhanced heating not only relative to their surroundings but relative to the Maxwell-model prediction for a homogeneous medium at the plume temperature. These results have important implications for thermal feedbacks in Europa’s ice shell.To self-consistently determine how convection interacts with tidal heating that is correctly calculated from the time-evolving heterogeneous temperature field, we coupled viscoelastic simulations of oscillatory tidal flexing (using Tekton) to long-term simulations of the convective evolution (using ConMan). Our simulations show that the tidal dissipation rate resulting from heterogeneous temperature can have a strong impact on thermal convection in Europa’s ice shell. Temperatures within upwelling plumes are greatly enhanced and can reach the melting temperature under plausible tidal-flexing amplitude for Europa. A pre-existing fracture zone (at least 6 km deep) promotes the concentration of tidal dissipation (up to ∼20 times more than that in the surroundings), leading to lithospheric thinning. This supports the idea that spatially variable tidal dissipation could lead locally to high temperatures, partial melting, and play an important role in the formation of ridges, chaos, or other features.     

Two nearby M dwarf binaries from the Two Micron All Sky Survey

We report the discovery of two binary M dwarf systems in the immediate solar neighbourhood using the Two Micron All Sky Survey (2MASS). The first is an M6.5 companion to the nearby G star HD 86728 (Gl 376). The known properties of HD 86728 indicate that the M dwarf (Gl 376B) is old, metal-rich and only 14.9 parsec away. The M dwarf is highly active, with both H α and X-ray emission. Thus, Gl 376B offers the opportunity to study an old, bright, active M dwarf with known metallicity, age and luminosity. We show that it is probable that Gl 376B is itself an unresolved pair. The other system consists of an M6.5 and an M8 dwarf with 14.5 arcsec separation. We estimate a distance of ∼16 parsec for this very low-mass pair. Stronger activity is observed in the M6.5 dwarf, supporting evidence that chromospheric activity is weakening near the hydrogen-burning limit.     

Coupled convection and tidal dissipation in Europa’s ice shell using non-Newtonian grain-size-sensitive (GSS) creep rheology

We present self-consistent, fully coupled two-dimensional (2D) numerical models of thermal evolution and tidal heating to investigate how convection interacts with tidal dissipation under the influence of non-Newtonian grain-size-sensitive creep rheology (plausibly resulting from grain boundary sliding) in Europa’s ice shell. To determine the thermal evolution, we solved the convection equations (using finite-element code ConMan) with the tidal dissipation as a heat source. For a given heterogeneous temperature field at a given time, we determined the tidal dissipation rate throughout the ice shell by solving for the tidal stresses and strains subject to Maxwell viscoelastic rheology (using finite-element code Tekton). In this way, the convection and tidal heating are fully coupled and evolve together. Our simulations show that the tidal dissipation rate can have a strong impact on the onset of thermal convection in Europa’s ice shell under non-Newtonian GSS rheology. By varying the ice grain size (1-10 mm), ice-shell thickness (20-120 km), and tidal-strain amplitude (0-4 × 10⁻⁵), we study the interrelationship of convection and conduction regimes in Europa’s ice shell. Under non-Newtonian grain-size-sensitive creep rheology and ice grain size larger than 1 mm, no thermal convection can initiate in Europa’s ice shell (for thicknesses <100 km) without tidal dissipation. However, thermal convection can start in thinner ice shells under the influence of tidal dissipation. The required tidal-strain amplitude for convection to occur decreases as the ice-shell thickness increases. For grain sizes of 1-10 mm, convection can occur in ice shells as thin as 20-40 km with the estimated tidal-strain amplitude of 2 × 10⁻⁵ on Europa.