Markov Mandala I & II

This submission consists of two images that use artful graphic representation of data to illustrate how COVID-19 spreads across a series of discreet pivot points. Accompanying each image is a brief description and meditation describing the image and its meaning

Forgiveness of others and self-forgiveness In the context of interpersonal conflict

An integrative model of interpersonal conflict and forgiveness was proposed, and a small number of the relationships within the model were tested. The expectation was that for participants who reported an interpersonal conflict with a family member or friend the interaction of being able to forgive the other in the conflict (other-forgiveness), being able to forgive self in the conflict (self-forgiveness), and intensity of the conflict would predict personal resolution. Results indicated strong relationships between the main effects of other-forgiveness and self-forgiveness and personal resolution but no interaction effect. It was also expected that either high levels of other-forgiveness or self-forgiveness alone would predict false forgiveness. This was also not supported. Different post-hoc results were found for both personal resolution and false forgiveness hypotheses based on who the other party to the conflict was (family or friend)and intensity of self or other. The presence of relationships, although not as hypothesized, lent support for leaving all of the tested variables in the model. The need to reframe measures of relevant variables was also expressed

Properties of Umbral Dots as Measured from the New Solar Telescope Data and MHD Simulations

We studied bright umbral dots (UDs) detected in a moderate size sunspot and compared their statistical properties to recent MHD models. The study is based on high resolution data recorded by the New Solar Telescope at the Big Bear Solar Observatory and 3D MHD simulations of sunspots. Observed UDs, living longer than 150 s, were detected and tracked in a 46 min long data set, using an automatic detection code. Total 1553 (620) UDs were detected in the photospheric (low chromospheric) data. Our main findings are: i) none of the analyzed UDs is precisely circular, ii) the diameter-intensity relationship only holds in bright umbral areas, and iii) UD velocities are inversely related to their lifetime. While nearly all photospheric UDs can be identified in the low chromospheric images, some small closely spaced UDs appear in the low chromosphere as a single cluster. Slow moving and long living UDs seem to exist in both the low chromosphere and photosphere, while fast moving and short living UDs are mainly detected in the photospheric images. Comparison to the 3D MHD simulations showed that both types of UDs display, on average, very similar statistical characteristics. However, i) the average number of observed UDs per unit area is smaller than that of the model UDs, and ii) on average, the diameter of model UDs is slightly larger than that of observed ones.Comment: Accepted by the AP

The Role of Subsurface Flows in Solar Surface Convection: Modeling the Spectrum of Supergranular and Larger Scale Flows

We model the solar horizontal velocity power spectrum at scales larger than granulation using a two-component approximation to the mass continuity equation. The model takes four times the density scale height as the integral (driving) scale of the vertical motions at each depth. Scales larger than this decay with height from the deeper layers. Those smaller are assumed to follow a Kolomogorov turbulent cascade, with the total power in the vertical convective motions matching that required to transport the solar luminosity in a mixing length formulation. These model components are validated using large scale radiative hydrodynamic simulations. We reach two primary conclusions: 1. The model predicts significantly more power at low wavenumbers than is observed in the solar photospheric horizontal velocity spectrum. 2. Ionization plays a minor role in shaping the observed solar velocity spectrum by reducing convective amplitudes in the regions of partial helium ionization. The excess low wavenumber power is also seen in the fully nonlinear three-dimensional radiative hydrodynamic simulations employing a realistic equation of state. This adds to other recent evidence suggesting that the amplitudes of large scale convective motions in the Sun are significantly lower than expected. Employing the same feature tracking algorithm used with observational data on the simulation output, we show that the observed low wavenumber power can be reproduced in hydrodynamic models if the amplitudes of large scale modes in the deep layers are artificially reduced. Since the large scale modes have reduced amplitudes, modes on the scale of supergranulation and smaller remain important to convective heat flux even in the deep layers, suggesting that small scale convective correlations are maintained through the bulk of the solar convection zone.Comment: 36 pages, 6 figure

Thermal Pressurization and Onset of Melting in Fault Zones

We examine how frictional heating drives the evolution of temperature, strength, and fracture energy during earthquake slip. For small slip distances, heat and pore fluid are unable to escape the shearing fault core, and the behavior is well approximated by simple analytical models that neglect any transport. Following large slip distances, the finite width of the shear zone is small compared to the thicknesses of the thermal and hydrological boundary layers, and the fault behavior approaches that predicted for the idealized case of slip on a plane. To evaluate the range in which the predictions of these two sets of approximations are valid, we develop a model that describes how frictional dissipation within a finite shear zone drives heat and mass transport through the surrounding static gouge. With realistic parameter values and slips greater than a few centimeters, the subsequent evolution of strength and fracture energy are approximated well by the planar slip model. However, the temperature evolution is much more sensitive to the finite shear zone thickness, and the ultimate temperature rise tends to be intermediate between that predicted for the two simplified cases. We explore the range of conditions necessary for melting to begin and focus in particular on the potential role of fault zone damage in facilitating fluid transport and promoting larger temperature increases. We discuss how the apparent scarcity of exhumed pseudotachylytes places constraints on some of the more uncertain fault zone parameters.Earth and Planetary SciencesEngineering and Applied Science

Thresholds in the sliding resistance of simulated basal ice

We report laboratory determinations of the shear resistance to sliding melting ice with entrained particles over a hard, impermeable surface. With higher particle concentrations and larger particle sizes, Coulomb friction at particle-bed contacts dominates and the shear stress increases linearly with normal load. We term this the <i>sandy</i> regime. When either particle concentration or particle size is reduced below a threshold, the dependence of shear resistance on normal load is no longer statistically significant. We term this regime <i>slippery</i>. We use force and mass balance considerations to examine the flow of melt water beneath the simulated basal ice. At high particle concentrations, the transition from sandy to slippery behavior occurs when the particle size is comparable to the thickness of the melt film that separates the sliding ice from its bed. For larger particle sizes, a transition from <i>sandy</i> to <i>slippery</i> behavior occurs when the particle concentration drops sufficiently that the normal load is no longer transferred completely to the particle-bed contacts. We estimate that the melt films separating the particles from the ice are approximately 0.1 µm thick at this transition. Our laboratory results suggest the potential for abrupt transitions in the shear resistance beneath hard-bedded glaciers with changes in either the thickness of melt layers or the particle loading

Helioseismic detection of deep meridional flow

Steady meridional flow makes no first-order perturbation to the frequencies of helioseismic normal modes. It does, however, Doppler shift the local wavenumber, thereby distorting the eigenfunctions. For high-degree modes, whose peaks in a power spectrum are blended into continuous ridges, the effect of the distortion is to shift the locations of those ridges. From this blended superposition of modes, one can isolate oppositely directed wave components with the same local horizontal wavenumber and measure a frequency difference which can be safely used to infer the subsurface background flow. But such a procedure fails for the components of the more-deeply-penetrating low-degree modes that are not blended into ridges. Instead, one must analyze the spatial distortions explicitly. With a simple toy model, we illustrate one method by which that might be accomplished by measuring the spatial variation of the oscillation phase. We estimate that by this procedure it might be possible to infer meridional flow deep in the solar convection zone.Comment: 23 pages, 9 color figures, submitted to the Astrophysical Journa

Chaotic saddles in nonlinear modulational interactions in a plasma

A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.Comment: Physics of Plasmas, in pres

The generalized Clapeyron equation and its application to confined ice growth

Most theoretical descriptions of stresses induced by freezing are rooted in the (generalized) Clapeyron equation, which predicts the pressure that a solid can exert as it cools below its melting temperature. This equation is central for topics ranging beyond glaciology to geomorphology, civil engineering, food storage, and cryopreservation. However, it has inherent limitations, requiring isotropic solid stresses and conditions near bulk equilibrium. Here, we examine when the Clapeyron equation is applicable by providing a rigorous derivation that details all assumptions. We demonstrate the natural extension for anisotropic stress states, and we show how the temperature and pressure ranges for validity depend on well-defined material properties. Finally, we demonstrate how the range of applicability of the (linear) Clapeyron equation can be extended by adding higher-order terms, yielding results that are in good agreement with experimental data for the pressure melting of ice.Comment: 2 Figure