Pascal Principle for Diffusion-Controlled Trapping Reactions

"All misfortune of man comes from the fact that he does not stay peacefully in his room", has once asserted Blaise Pascal. In the present paper we evoke this statement as the "Pascal principle" in regard to the problem of survival of an "A" particle, which performs a lattice random walk in presence of a concentration of randomly moving traps "B", and gets annihilated upon encounters with any of them. We prove here that at sufficiently large times for both perfect and imperfect trapping reactions, for arbitrary spatial dimension "d" and for a rather general class of random walks, the "A" particle survival probability is less than or equal to the survival probability of an immobile target in the presence of randomly moving traps.Comment: 4 pages, RevTex, appearing in PR

Traveling wave fronts and the transition to saturation

We propose a general method to study the solutions to nonlinear QCD evolution equations, based on a deep analogy with the physics of traveling waves. In particular, we show that the transition to the saturation regime of high energy QCD is identical to the formation of the front of a traveling wave. Within this physical picture, we provide the expressions for the saturation scale and the gluon density profile as a function of the total rapidity and the transverse momentum. The application to the Balitsky-Kovchegov equation for both fixed and running coupling constants confirms the effectiveness of this method.Comment: 9 pages, 3 figures, references adde

Lattice theory of trapping reactions with mobile species

We present a stochastic lattice theory describing the kinetic behavior of trapping reactions $A + B \to B$, in which both the $A$ and $B$ particles perform an independent stochastic motion on a regular hypercubic lattice. Upon an encounter of an $A$ particle with any of the $B$ particles, $A$ is annihilated with a finite probability; finite reaction rate is taken into account by introducing a set of two-state random variables - "gates", imposed on each $B$ particle, such that an open (closed) gate corresponds to a reactive (passive) state. We evaluate here a formal expression describing the time evolution of the $A$ particle survival probability, which generalizes our previous results. We prove that for quite a general class of random motion of the species involved in the reaction process, for infinite or finite number of traps, and for any time $t$, the $A$ particle survival probability is always larger in case when $A$ stays immobile, than in situations when it moves.Comment: 12 pages, appearing in PR

Random Convex Hulls and Extreme Value Statistics

In this paper we study the statistical properties of convex hulls of $N$ random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem, we present a unifying approach, based on the notion of support function of a closed curve and the associated Cauchy's formulae, that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points. Our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics. As an example of correlated points, we study here in detail the case when the points represent the vertices of $n$ independent random walks. In the continuum time limit this reduces to $n$ independent planar Brownian trajectories for which we compute exactly, for all $n$, the mean perimeter and the mean area of their global convex hull. Our results have relevant applications in ecology in estimating the home range of a herd of animals. Some of these results were announced recently in a short communication [Phys. Rev. Lett. {\bf 103}, 140602 (2009)].Comment: 61 pages (pedagogical review); invited contribution to the special issue of J. Stat. Phys. celebrating the 50 years of Yeshiba/Rutgers meeting

A comparative view of glacial and periglacial landforms on Earth and Mars

This paper emphasizes the importance of using terrestrial analogues to improve our understanding of the role of ice on Mars through its associated landforms. We discuss terrestrial regions and techniques that can help understand Martian icy environments, and highlight the necessity to explore the Martian cryosphere as the next natural step

Reexamining the Potential to Classify Lava Flows From the Fractality of Their Margins

Can fractal analysis of a lava flow's margin enable classification of the lava's morphologic type (e.g., pāhoehoe)? Such classifications would provide insights into the rheology and dynamics of the flow when it was emplaced. The potential to classify lava flows from remotely-sensed data would particularly benefit the analysis of flows that are inaccessible, including flows on other planetary bodies. The technique's current interpretive framework depends on three assumptions: (1) measured margin fractality is scale-invariant; (2) morphologic types can be uniquely distinguished based on measured margin fractality; and (3) modification of margin fractality by topography, including substrate slope and confinement, would be minimal or independently recognizable. We critically evaluate these assumptions at meter scales (1–10 m) using 15 field-collected flow margin intervals from a wide variety of morphologic types in Hawaiʻi, Iceland, and Idaho. Among the 12 margin intervals that satisfy the current framework's suitability criteria (e.g., geomorphic freshness, shallowly-sloped substrates), we show that five exhibit notably scale-dependent fractality and all five from lava types other than ‘a‘ā or pāhoehoe would be classified as one or both of those types at some scales. Additionally, an ‘a‘ā flow on a 15° slope (Mauna Ulu, Hawaiʻi) and a spiny pāhoehoe flow confined by a stream bank (Holuhraun, Iceland) exhibit significantly depressed fractalities but lack diagnostic signatures for these modifications. We therefore conclude that all three assumptions of the current framework are invalid at meter scales and propose a new framework to leverage the potential of the underlying fractal technique while acknowledging these complexities. © 2021. American Geophysical Union. All Rights Reserved.6 month embargo; first published: 25 March 2021This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

North polar trough formation due to in-situ erosion as a source of young ice in mid-latitudinal mantles on Mars

The clockwise spiral of troughs marking the Martian north polar plateau forms one of the planet’s youngest megastructures. One popular hypothesis posits that the spiral pattern resulted as troughs underwent poleward migration. Here, we show that the troughs are extensively segmented into enclosed depressions (or cells). Many cell interiors display concentric layers that connect pole- and equator-facing slopes, demonstrating in-situ trough erosion. The segmentation patterns indicate a history of gradual trough growth transversely to katabatic wind directions, whereby increases in trough intersections generated their spiral arrangement. The erosional event recorded in the truncated strata and trough segmentation may have supplied up to ~25% of the volume of the mid-latitude icy mantles. Topographically subtle undulations transition into troughs and have distributions that mimic and extend the troughs’ spiraling pattern, indicating that they probably represent buried trough sections. The retention of the spiral pattern in surface and subsurface troughs is consistent with the megastructure’s stabilization before its partial burial. A previously suggested warm paleoclimatic spike indicates that the erosion could have occurred as recently as ~50 Ka. Hence, if the removed ice was redeposited to form the mid-latitude mantles, they could provide a valuable source of near-surface, clean ice for future human exploration. © 2021, The Author(s).Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Burial Depths of Extensive Shallow Cryptomaria in the Lunar Schiller–Schickard Region

Quantifying the volumes and geologic nature of lunar volcanic eruptions is important for constraining the thermal and geologic evolution of the Moon. Cryptomaria are effusive, basaltic lava flows on the Moon that were subsequently buried, and therefore hidden, by higher-albedo basin and crater ejecta. Radar offers the ability to probe the subsurface for geologic units not otherwise apparent at the surface. We use Arecibo/Green Bank Observatory and Lunar Reconnaissance Orbiter Mini-RF radar data sets to characterize maria and cryptomaria within the Schiller–Schickard region. We find significant variability in the radar backscatter across the region that does not correspond to previously mapped boundaries of maria and cryptomaria in the literature. We use the characteristic low backscatter (due to the attenuating nature in radio waves of some basaltic minerals) to analyze the distribution of cryptomaria. We use the reduction in radar backscatter to estimate burial depths of cryptomaria across the area. We present a new map of Schiller–Schickard cryptomaria and the local variability in the thicknesses of the light plains that bury the basalts. We find burial depths ranging from >100 m in the deepest areas to just a few to tens of meters in areas with shallow cryptomaria (particularly prominent in the southeast). These areas are generally contiguous with maria, allowing us to track mare lava flow units into the subsurface at mare/highland margins. We propose that ∼67% of the region contains surface or buried basaltic volcanism, which represents over twice (2.7× increase) the areal extent of cryptomaria reported in previous studies. © 2022. The Author(s). Published by the American Astronomical Society.Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Approach-avoidance decisions under threat: The role of autonomic psychophysiological states

Contains fulltext : 231749.pdf (publisher's version ) (Open Access)Acutely challenging or threatening situations frequently require approach-avoidance decisions. Acute threat triggers fast autonomic changes that prepare the body to freeze, fight or flee. However, such autonomic changes may also influence subsequent instrumental approach-avoidance decisions. Since defensive bodily states are often not considered in value-based decision-making models, it remains unclear how they influence the decision-making process. Here, we aim to bridge this gap by discussing the existing literature on the potential role of threat-induced bodily states on decision making and provide a new neurocomputational framework explaining how these effects can facilitate or bias approach-avoid decisions under threat. Theoretical accounts have stated that threat-induced parasympathetic activity is involved in information gathering and decision making. Parasympathetic dominance over sympathetic activity is particularly seen during threat-anticipatory freezing, an evolutionarily conserved response to threat demonstrated across species and characterized by immobility and bradycardia. Although this state of freezing has been linked to altered information processing and action preparation, a full theoretical treatment of the interactions with value-based decision making has not yet been achieved. Our neural framework, which we term the Threat State/Value Integration (TSI) Model, will illustrate how threat-induced bodily states may impact valuation of competing incentives at three stages of the decision-making process, namely at threat evaluation, integration of rewards and threats, and action initiation. Additionally, because altered parasympathetic activity and decision biases have been shown in anxious populations, we will end with discussing how biases in this system can lead to characteristic patterns of avoidance seen in anxiety-related disorders, motivating future pre-clinical and clinical research.12 p

The Mars orbiter for resources, ices, and environments (MORIE) science goals and instrument trades in radar, imaging, and spectroscopy

The Mars Orbiter for Resources, Ices, and Environments (MORIE) was selected as one of NASA’s 2019 Planetary Mission Concept Studies. The mission builds upon recent discoveries and current knowledge gaps linked to two primary scientific questions: (1) when did elements of the cryosphere form and how are ice deposits linked to current, recent, and ancient climate, and (2) how does the crust record the evolution of surface environments and their transition through time? Addressing these questions has emerged in numerous recent reports as a high priority in investigating the evolution of Mars as a habitable world. A subsidiary goal of the mission concept is to provide information relevant to the eventual human exploration of Mars, specifically helping to locate and quantify near-surface water ice and hydrated mineral resources. The proposed instrument suite includes polarimetric synthetic aperture radar imaging, radar sounding, high-resolution visible and infrared imaging, both short-wave and thermal-infrared spectroscopy, and multichannel wide-angle imaging. MORIE would provide novel measurements of Mars expected to lead to significant new discoveries by the first radar imaging from orbit, radar sounding directly over the poles, and mineral mapping at spatial scales that will unravel geologic sequence stratigraphy through time. The final report of the mission concept provides details on the spacecraft, orbital design, technological maturity, results from systems-level integration studies, and costs. This article is intended to expand upon the science motivation for the mission, the measurement goals and objectives, and the instrument trade space that was examined in detail during the concept study. © 2021. The Author(s). Published by the American Astronomical Society.Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]